3.17: Comparison of Store, Catalog, and Internet Channels
- Compare and contrast the benefits of store, catalog, and internet channels
The most pronounced difference between store and non-store retail channels is the cost structure. Retail stores have comparatively higher costs than their non-store counter-parts because their costs include rent, utilities, inventory, and staffing. By comparison, non-store retail outlets have eliminated rent and utilities and greatly reduced carried inventory and staffing.
It’s for this reason that non-store retailing is used by established brick & mortar retailers to expand channels with a “brick & click” model and by entrepreneurial firms developing a pure play distribution channel, which is exclusively through e-commerce. It shouldn’t be assumed that non-store channels are without costs of their own. There are many specific to catalogs and e-commerce, which we’ll discuss below. However, they pale in comparison to the costs of brick & mortar retail.
Catalogs, when effective, are high-involvement marketing materials. Consumers leaf through the pages reviewing wide product assortments. As such, they have long been used as a marketing device to drive phone and in-store sales. But as online retail has continued to grow, catalog sales have eroded. No longer are catalogs the most effective or convenient methods for developing at-home sales; their place as a marketing tool has been under scrutiny.
Yet, some industry experts note that catalogs are changing–a reflection of their evolving role in the retail landscape and with the assumption that lower delivered mail volume means they’ll get more attention. Interestingly, in a survey on its website, Land’s End found that 75% of customers making a purchase had reviewed the catalog first. [1] . This might imply that catalogs have a complementary role with e-commerce. Perhaps, in being reimagined, they will become resources to merchandise products through visual narratives and encourage consumer engagement.
Of course, catalogs carry their own unique costs, which shouldn’t be overlooked. Chief among these are creation, photography, copy, layout, and design. Further, there are printing and mailing costs to be considered. These are not insignificant, to be sure. Yet, retailers like Costco, Nordstrom, William-Sonoma, and others combine to send over 10 billion catalogs annually in the U.S.
E-commerce refers to buying or selling products and services online or over the internet on retailers’ Web sites or mobile apps, or through marketplaces such as on Amazon or AliBaba. Given our own experience with e-commerce, it might be tempting to oversimplify the channel. But, it’s important to understand the interactions and activities at-play, as these reflect some of the implicit costs.
For example, digital marketing, including both Search Engine Optimization (SEO) and Search Engine Marketing (SEM) is used to connect sellers with potential buyers (Some social media platforms can also be used for the same ends). SEO requires web development, optimization, and maintenance to ensure the online visibility of a firm’s website in natural or organic search. SEM is a form of paid advertising that increases the visibility of a firm’s website in search engine results, such as through Google or Bing. Firms bid on keywords to ensure that when searches using those keywords are made, their website appears among the search results.
Individual shopping interactions may be supported by live chat or chatbots on websites. Regardless, transactions require online transaction processing, including electronic funds transfer and inventory management. Further, the collected data on the transaction and shopper may be warehoused in a database for future customer relationship management (CRM) initiatives. These support tools require investment and maintenance, which are costs that should not be overlooked.
Contributors and Attributions
- Comparison of Store, Catalog, and Internet Channels. Authored by : Patrick Williams. Provided by : Lumen Learning. License : CC BY: Attribution
- Amazon Logo. Provided by : Amazon. License : Public Domain: No Known Copyright


1.7: Coordinate Systems
By the end of this section, you will be able to
- Identify the key differences between Cartesian, cylindrical, and spherical systems.
The coordinate systems most commonly used in scientific and engineering analysis are the Cartesian [1], cylindrical [2], and spherical [3] systems. These systems are illustrated in Figures \(\PageIndex{1}\), \(\PageIndex{2}\), and \(\PageIndex{3}\), respectively.
Note that the use of variables is not universal; in particular, it is common to encounter the use of \(r\) in lieu of \(\rho\) for the radial coordinate in the cylindrical system, and the use of \(R\) in lieu of \(r\) for the radial coordinate in the spherical system. The angle \(\phi \) is typically called the azimuthal coordinate in both the cylindrical and spherical coordinates, while the angle \(\theta \) is typically called the polar coordinate in spherical coordinates. In contrast to Cartesian coordinates, in which the coordinate unit vectors \(\hat{x}\), \(\hat{y}\), \(\hat{z}\) always point in the same direction, the unit vectors in cylindrical and spherical coordinates will change direction based on the point in space that is being referenced, as indicated in the figures.
References
- Wikipedia contributors. Cartesian coordinate system [Internet]. Wikipedia, The Free Encyclopedia.
- Wikipedia contributors. Cylindrical coordinate system [Internet]. Wikipedia, The Free Encyclopedia.
- Wikipedia contributors. Spherical coordinate syste m [Internet]. Wikipedia, The Free Encyclopedia.
- Wikimedia Commons contributors. File: M0006 fCartesianBasis.svg [Internet]. Wikimedia Commons. (CC BY-SA 4.0; K. Kikkeri)
- Wikimedia Commons contributors. File: M0096 fCylindricalCoordinates.svg [Internet]. Wikimedia Commons. (CC BY-SA 4.0; K. Kikkeri)
- Wikimedia Commons contributors. File: Spherical Coordinate System.svg [Internet]. Wikimedia Commons. (CC BY-SA 4.0; K. Kikkeri)


5.7: Gestalt Principles of Perception
Learning Objectives
- Explain the figure-ground relationship
- Define Gestalt principles of grouping
- Describe how perceptual set is influenced by an individual’s characteristics and mental state
In the early part of the \(20^{th}\) century, Max Wertheimer published a paper demonstrating that individuals perceived motion in rapidly flickering static images—an insight that came to him as he used a child’s toy tachistoscope. Wertheimer, and his assistants Wolfgang Köhler and Kurt Koffka, who later became his partners, believed that perception involved more than simply combining sensory stimuli. This belief led to a new movement within the field of psychology known as Gestalt psychology . The word gestalt literally means form or pattern, but its use reflects the idea that the whole is different from the sum of its parts. In other words, the brain creates a perception that is more than simply the sum of available sensory inputs, and it does so in predictable ways. Gestalt psychologists translated these predictable ways into principles by which we organize sensory information. As a result, Gestalt psychology has been extremely influential in the area of sensation and perception (Rock & Palmer, 1990).
One Gestalt principle is the figure-ground relationship . According to this principle, we tend to segment our visual world into figure and ground. Figure is the object or person that is the focus of the visual field, while the ground is the background. As the figure shows, our perception can vary tremendously, depending on what is perceived as figure and what is perceived as ground. Presumably, our ability to interpret sensory information depends on what we label as figure and what we label as ground in any particular case, although this assumption has been called into question (Peterson & Gibson, 1994; Vecera & O’Reilly, 1998).
Another Gestalt principle for organizing sensory stimuli into meaningful perception is proximity . This principle asserts that things that are close to one another tend to be grouped together, as the figure below illustrates.
How we read something provides another illustration of the proximity concept. For example, we read this sentence like this, notl iket hiso rt hat. We group the letters of a given word together because there are no spaces between the letters, and we perceive words because there are spaces between each word. Here are some more examples: Cany oum akes enseo ft hiss entence? What doth es e wor dsmea n?
We might also use the principle of similarity to group things in our visual fields. According to this principle, things that are alike tend to be grouped together. For example, when watching a football game, we tend to group individuals based on the colors of their uniforms. When watching an offensive drive, we can get a sense of the two teams simply by grouping along this dimension.
Two additional Gestalt principles are the law of continuity (or good continuation ) and closure . The law of continuity suggests that we are more likely to perceive continuous, smooth flowing lines rather than jagged, broken lines figure \(\PageIndex{4}\). The principle of closure states that we organize our perceptions into complete objects rather than as a series of parts, figure \(\PageIndex{5}\).
According to Gestalt theorists, pattern perception , or our ability to discriminate among different figures and shapes, occurs by following the principles described above. You probably feel fairly certain that your perception accurately matches the real world, but this is not always the case. Our perceptions are based on perceptual hypotheses : educated guesses that we make while interpreting sensory information. These hypotheses are informed by a number of factors, including our personalities, experiences, and expectations. We use these hypotheses to generate our perceptual set. For instance, research has demonstrated that those who are given verbal priming produce a biased interpretation of complex ambiguous figures (Goolkasian & Woodbury, 2010).
DIG DEEPER: The Depths of Perception - Bias, Prejudice, and Cultural Factors
In this chapter, you have learned that perception is a complex process. Built from sensations, but influenced by our own experiences, biases, prejudices, and cultures , perceptions can be very different from person to person. Research suggests that implicit racial prejudice and stereotypes affect perception. For instance, several studies have demonstrated that non-Black participants identify weapons faster and are more likely to identify non-weapons as weapons when the image of the weapon is paired with the image of a Black person (Payne, 2001; Payne, Shimizu, & Jacoby, 2005). Furthermore, White individuals’ decisions to shoot an armed target in a video game is made more quickly when the target is Black (Correll, Park, Judd, & Wittenbrink, 2002; Correll, Urland, & Ito, 2006). This research is important, considering the number of very high-profile cases in the last few decades in which young Blacks were killed by people who claimed to believe that the unarmed individuals were armed and/or represented some threat to their personal safety.
Summary
Gestalt theorists have been incredibly influential in the areas of sensation and perception. Gestalt principles such as figure-ground relationship, grouping by proximity or similarity, the law of good continuation, and closure are all used to help explain how we organize sensory information. Our perceptions are not infallible, and they can be influenced by bias, prejudice, and other factors.
Glossary
- closure
- organizing our perceptions into complete objects rather than as a series of parts
- figure-ground relationship
- segmenting our visual world into figure and ground
- Gestalt psychology
- field of psychology based on the idea that the whole is different from the sum of its parts
- good continuation
- (also, continuity) we are more likely to perceive continuous, smooth flowing lines rather than jagged, broken lines
- pattern perception
- ability to discriminate among different figures and shapes
- perceptual hypothesis
- educated guess used to interpret sensory information
- principle of closure
- organize perceptions into complete objects rather than as a series of parts
- proximity
- things that are close to one another tend to be grouped together
- similarity
- things that are alike tend to be grouped together
Contributors and Attributions
-
Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact<EMAIL_ADDRESS>.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


10.3: Intersectionality
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- Erika Gutierrez, Janét Hund, Shaheen Johnson, Carlos Ramos, Lisette Rodriguez, & Joy Tsuhako
- Long Beach City College, Cerritos College, & Saddleback College via ASCCC Open Educational Resources Initiative (OERI)
Muslim Women and Hijab
The role of women in the Muslim community has received a good amount of attention. One such area of focused attention is in standards of dress. Islam stresses that women should be protected and must present themselves in a modest way while in public. The prophet Muhammad indicated that the female body should be covered with loose fitting clothing with the exception of the face, hands, and feet. Hijab refers to garments that allow women to adhere to the guidelines of modest dress. Hijab may include head or face covering as well as other garments worn to maintain modesty.
If and how women cover themselves varies from person to person, from country to country and among various religious sects. Some Muslim women simply do not practice hijab. Some wear hijabs that loosely cover their hair and neck. Other women may wear very full coverings that conceal almost their entire bodies.
Some in western societies view hijab as a symbol of oppression, a means for making women fade into the background of society. However, many Muslim women view it as a symbol of their identity, their strength, their beliefs, their values, and their respect for their bodies. For many Muslim women, these are not oppressive garments, but rather liberating garments, that free them from being regarded as a sexual object. In fact, in the second half of the twentieth century, the practice of veiling increased among Muslim women in the Middle East as well as around the world (Ahmed, 2011). Hijab has not only become more common among Muslim women, but has emerged as an important symbolic representation of Islamic feminism.
Islamic Feminism
Fatema Mernissi
Fate Mernissi (1940-2015) was a Moroccan feminist writer and sociologist, with her work focusing on a voice for the oppressed and marginalized women. Her legacy can be greatly attributed to her scholarly and literary contributions to the early feminist movement, as she tackles issues such as Eurocentrism, intersectionality, transnationalism, and global feminism.
Mernissi is known for her sociolopolitical approaches towards discussing gender and sexual identities, specifically those of which are focused within Morocco. She became known internationally mainly as an Islamic feminist. She authored Beyond the Veil in 1975. In her writings, she was largely concerned with Islam and women's roles in it, analyzing the historical development of Islamic thought and its modern manifestation. Through a detailed investigation of the nature of the succession to Muhammed, she cast doubt on the validity of some of the hadith (sayings and traditions attributed to him), and therefore the subordination of women that she sees in Islam, but not necessarily in the Quran.
A recurring topic for multiple of her writings is Scheherazde and the digital sphere, as she explores cases in which women take part in online media outlets. In these writings, she mentioned how technology is quickly spreading - via the Internet - and analyzes the roles and contributions of women in this movement.
She also wrote about life within harems, gender, and public and private spheres. In one of her articles, Size 6: The Western Women's Harem, she discusses the repression and pressures women face merely based on their physical appearance. Whether in Moroccan society or the West, she surmises that women must live up to stereotypical standards such as dress sizes (e.g. size 6) and that these practices isolate and mistreat women. Later, in her book, Islam and Democracy: Fear of the Modern World, Mernissi she looks at how fundamentalism controlled what a woman would be able to wear, so a democratic society that freed women to dress as they pleased could appear threatening to a hyper-masculine culture.
Additionally, she notes that Muslim women were not victims of their religious practices any more than Western women were victims of the patriarchy; both groups of women were oppressed by specific social intitutions within a religion or society created to profit off of the marginalization of others. She explains that Western women were veiled, just as Muslim women were, yet Western veils were much more discreet. To her, youth and beauty veiled Western women, and once a woman no longer had these, she was hardly recognized by society.
Mernissi's work highlighted how Western feminism could be detrimental to the empowerment of women around the globe if it lacked an intersectional approach to women's issues. In her book, The Forgotten Queens of Islam, she uses an intersectional lens to understand the positions of women throughout early Islamic history through social and political identities that created modes of discrimination. Her aim was to bring to light the significant contributions that women had throughout early Islamic history and debunk the misconceptions about the absence of women as political and authoritative figures. She did this through exploring leadership roles that women were involved in throughout Islamic history, including accounts of 15 women and the active roles they played in pre-modern Islam politics.
In her book Women's Rebellion & Islamic Memory, Mernissi analyzes the role of women in relation to the world of contemporary Islam and how the state ultimately supports inequality. She argues that the freedom from these controlling traditions and expectations of women is the only way for the Arab world to develop. In her book, Islam and Democracy, she suggests ways in which progressive Muslims, including feminists, who choose to advocate for democracy and resist fundamentalism should draw from the same sacred texts as those who seek to oppress them, in order to prove that Islam is not fundamentally against women.
Feminism is often thought of as incompatible and categorically opposed to the cultural and religious traditions of Islam. The truth, however, is that Muslim women have been active in feminist movements and ideals for many years. In fact, research has shown that one in four Arab Muslims supports feminism (Glas and Alexander, 2020). Just as feminism in the West has given women a voice and an opportunity to challenge gender inequality in society, so too has feminism among Muslim women. All social movements are unique to the social and cultural context in which they arise, and Islamic feminism is no exception. Muslim women have adapted their own strategies for countering gender oppression, while at the same time working within an Islamic framework. Thus balancing their feminist ideals with the religious beliefs they hold dear.
The Centre for Muslim Minorities and Islam Policy Studies defines a Muslim feminist as "one who adopts a worldview in which Islam can be contextualized and reinterpreted in order to promote concepts of equity and equality between men and women; and for whom freedom of choice plays an important part in expression of faith." The term "Islamic feminism" distinguishes those women who work specifically within the Islamic faith, as opposed to “secularist feminism” which is weakly attached to religion or not at all.
A basic tenant of Islamic feminism is that at its core, it draws upon the Quranic concept of equality of all human beings, and insists on the application of this theology to both the public and private spheres. Muslim feminists argue that the oppressive practices - to which women in the Middle East are subjected - are caused by the prevalence of patriarchal interpretations of Islam, rather than Islam itself (Ahmed, 1992). Thus Muslim feminists strive to balance cultural and religious traditions, while articulating and fighting for their feminist concerns, defining and developing feminism and feminist practices on their own terms. Just as Muslim women do, Jewish women have also strived to balance feminism and faith.
Jewish Feminism
Jewish feminism is a movement that seeks to make the religious, legal, and social status of Jewish women equal to that of Jewish men. Feminist movements, with varying approaches and successes, have opened up within all major branches of the Jewish religion.
In its modern form, the Jewish feminist movement can be traced to the early 1970s. Judith Plaskow, known for being the first Jewish feminist theologian, claims the main grievances of early Jewish feminists were women's exclusion from the minyan (all male prayer group), women's exemption from mitzvot (the 613 commandments given in the Torah at Mount Sinai and the seven rabbinic commandments instituted later, for a total of 620), and women's inability to function as witnesses and to initiate divorce in Jewish religious courts (Plaskow, 2003). The issue of divorce is expressed in the term agunah , which describes a woman whose husband refuses, or is unable, to grant her a divorce according to Jewish law.
Just as there are varying degrees to which Jews adhere to cultural and/or religious practices, so too are there various versions of feminist theologies that exist within the Jewish Community. For example, Orthodox Jewish feminism seeks to change the position of women from within Jewish law. Orthodox feminists work with rabbis and rabbinical institutions to create more inclusive practices within Orthodox communal life and leadership. Orthodox feminism tends to focus on issues such as fostering women's education, leadership, ritual participation, and making synagogue more women friendly. Some branches of Jewish feminism focus on the gender polarity that exists in the religious and cultural practices within the Jewish community. While Orthodox feminists strive for women's rights and opportunities, they do so within the framework of Jewish law.
Bella Savitzky Abzug (1920-1998), born to an Orthodox Russian Jewish family in New York City, was a social activist, U.S. Representative, and a leader in the women's movement in the United States. She worked alongside other feminists such as Gloria Steinem, Shirley Chisholm, and Betty Friedan to found the National Women's Political Caucus. She attributed her inclination towards feminism to her time spent at synagogue. According to Azbug, "It was during these visits to the synagogue that I think I had my first thoughts as a feminist rebel. I didn't like the fact that women were consigned to the back rows of the balcony."
LGBTQIA+ Rights
Lesbian, gay, bisexual and transgender citizens generally have limited or highly restrictive rights in most parts of the Middle East, and are open to hostility in others. Sex between men is illegal in 10 of the 18 countries that make up the region. It is punishable by death in 6 of these 18 countries. The rights and freedoms of LGBTQIA+ citizens are strongly influenced by the prevailing cultural traditions and religious mores of people living in the region – particularly Islam. Several Middle Eastern countries have received strong international criticism for persecuting homosexuality and transgender people by fines, imprisonment and death.
Male same sex activity is illegal and punishable by imprisonment in Kuwait, Egypt, Oman, Qatar, and Syria. It is punishable by death in Iran, Saudi Arabia, Qatar, and the United Arab Emirates. In Yemen or Palestine (Gaza Strip) the punishment might differ between death and imprisonment depending on the act committed. Even though laws against female same sex activity are less strict, few countries recognize legal rights and provisions.
In the United States, LGBTQIA+ Middle Eastern Americans face a unique challenge. On the one hand, there is the challenge of post 9/11 attitudes and discrimination toward Muslim Americans. As Muslim society is still, by and large, heteronormative, there is also the challenge of hostility, harassment or discrimination that may be experienced from the the Middle Eastern community at large.
Contributors and Attributions
- Rodriguez, Lisette. (Long Beach City College)
- Ramos, Carlos. (Long Beach City College)
- Bella Abzug (Wikipedia) ( CC BY-SA 3.0 )
- Fatema Mernissi (Wikipedia) ( CC BY-SA 3.0 )
- Jewish Feminism (Wikipedia) ( CC BY-SA 3.0 )
- LGBT Rights in the Middle East (Wikipedia) ( CC BY-SA 3.0 )
Works Cited
- Ahmed, L. (1992). Women and Gender in Islam . New Haven, CT: Yale University Press.
- Ahmed, L. (2011). Quiet Revolution: The Veil's Resurgence from the Middle East to America. New Haven, CT: Yale University Press.
- Glas, S. & Alexander, A. (2020). Explaining support for Muslim feminism in the Arab middle east and north Africa. Gender & Society, 34(3), 437–466.
- Plaskow, J. (2003). Jewish feminist thought. In D.H. Frank & O Leaman (Eds). History of Jewish Philosophy. London, UK: Routledge.
- Independent Lens. (2020). Shadya. Independent Television Service, Public Broadcast Network.


6: Listening
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- 6.1: Introduction to Listening
- Listening may seem like a natural skill, but there is much more to this communicative act than it appears on the surface. To help you improve your own listening skills it requires that you have a better understanding of why listening is so important and what is involved in the listening process.
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- 6.2: Stages of the Listening Process
- Although listening may seem like it should be a fairly simple process, there are several steps to the listening process. Just as you learned in your chapter on perception, these steps occur so rapidly that we may not even realize we are doing them. The steps of the listening process that we will explore include receiving, interpreting, recalling, evaluating, and responding to messages.
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- 6.3: Functions of Listening
- We are sure that you have noticed that when you are watching a movie, or listening to music, that you are engaged differently than when you are listening to one of your professors. There is value in understanding that there are different functions of listening because we can then use the most appropriate listening skills to meet the purpose or occasion. Using these functions appropriately will lead to better engagement and understanding.
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- 6.5: Barriers to Listening
- A barrier to listening is anything that is hindering you from recognizing, understanding, and accurately interpreting the message that you are receiving. In this next section, we will discuss five different barriers to effective listening: Information overload, internal and external distractions, prejudice or prejudging, and rate of speech and thought.
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- 6.6: Ineffective Listening Practices
- Being aware or conscious of the habits we have is the first step to improving how we listen. This next section will look at ineffective listening practices that include pseudo-listening, selective listening, defensive listening, aggressive listening, narcissistic listening, insensitive listening, interrupting, and eavesdropping.
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- 6.7: Becoming a Better Listener
- The principles of active listening are not hard to understand, but they are hard to implement and require practice to use them effectively. Active listening is being engaged as a listener, not just hearing the words. Active listening requires purposefully focusing on what a speaker is saying with the objective of understanding. This final section of the chapter will describe what active listening means and the principles of active listening.
Thumbnail: CommScope Lifestyle Images on Flickr is licensed CC-BY-NC-ND 2.0


12: Linear Regression and Correlation
Regression analysis is a statistical process for estimating the relationships among variables and includes many techniques for modeling and analyzing several variables. When the focus is on the relationship between a dependent variable and one or more independent variables.
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- 12.1: Prelude to Linear Regression and Correlation
- In this chapter, you will be studying the simplest form of regression, "linear regression" with one independent variable (x). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.
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- 12.2: Linear Equations
- Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form: y=a+bx where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.
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- 12.3: Scatter Plots
- A scatter plot shows the direction of a relationship between the variables. A clear direction happens when there is either: High values of one variable occurring with high values of the other variable or low values of one variable occurring with low values of the other variable. High values of one variable occurring with low values of the other variable.
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- 12.4: The Regression Equation
- A regression line, or a line of best fit, can be drawn on a scatter plot and used to predict outcomes for the x and y variables in a given data set or sample data. There are several ways to find a regression line, but usually the least-squares regression line is used because it creates a uniform line. Residuals measure the distance from the actual value of y and the estimated value of y . The Sum of Squared Errors, when set to its minimum, calculates the points on the line of best fit.
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- 12.5: Testing the Significance of the Correlation Coefficient
- The correlation coefficient tells us about the strength and direction of the linear relationship between x and y. However, the reliability of the linear model also depends on how many observed data points are in the sample. We need to look at both the value of the correlation coefficient r and the sample size n, and perform a hypothesis test of the "significance of the correlation coefficient" to decide whether the linear relationship in the sample data is strong enough to use to linear model.
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- 12.6: Prediction
- After determining the presence of a strong correlation coefficient and calculating the line of best fit, you can use the least squares regression line to make predictions about your data. The process of predicting inside of the observed x values observed in the data is called interpolation. The process of predicting outside of the observed x-values observed in the data is called extrapolation.
Contributors and Attributions
-
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


1.13: Words of Wisdom - With a Little Help from My Friends
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Paulo Fernandes
Paulo Fernandes
We often hear about the importance of relationships: a necessary aspect of integration in society. Unfortunately, we rarely follow that advice. Perhaps we live an excessively busy life or we already have a close group of friends and do not feel compelled to meet new people. I have come to learn through my time in college that neglecting to cultivate new relationships is detrimental to living a happy and successful life. I would like to offer this piece of advice: no matter how difficult it seems at first, always try to make new friends . College is not always easy. However, having friends makes it much easier. Friends are a vital part of your life that can expose you to new subjects, cultures, and experiences while giving you the opportunity to do the same for them.
At my college, there was a small space that the students called “the bat cave.” It was by no means a first-class lounge, but it was a place where friends could help others better understand their course material. We gave it this peculiar nickname because it was our place to get together and conquer villains one after another. These were not your everyday super villains, however. Sometimes they were complicated homework assignments and other times they were difficult exams. No matter the challenge, someone was always willing to help. I went to the bat cave several times and every visit I learned something new. Professors and teaching assistants could not relate to us like our friends could. That made a difference, because nothing was better than being taught by a friend.
Friends are not only an essential support for your time in school, but also can be integral in helping realize post-college aspirations. During a visit to New York City, I visited the offices of the company Spotify. After touring their facilities I had the opportunity to talk to some of the employees. One man I talked with was a senior employee who worked at Microsoft prior to joining Spotify’s team. Our conversation stuck in my head because he gave a very striking piece of advice: make friends. It never truly occurred to me that the friends you make in college could impact your future in the workforce. They could be partners in potential business ventures or help you land your dream job. In any case, having strong connections with friends can undoubtedly make a major difference in your career.
The best part of making new friends, however, is trading life experiences, skills, and interests with them. For a year and a half before my final semester of college, I studied abroad in the United States. My family was concerned because typically, students search for first jobs prior to graduation. I, on the other hand, had no trepidation about going because I knew that I would have countless, exciting learning experiences. I can say today, without a doubt, that my trip was a great decision. I met incredible people, and through knowing them, I grew and changed. I also know that I was a positive feature in the lives of my new friends. The greatest thing that I learned was that meeting different people with different backgrounds, histories, perspectives, or even different musical tastes, inevitably changes you and lets you see the world in an entirely different way. You no longer see the world as simply a big, blue sphere with freezing winters or sizzling summers (although that certainly seems to be the case up North!), but as a place in which people like you live, learn, and love.
Going to college may seem hard, but it does not need to be. I have learned that the way I perceive my life as a student completely relies upon my relationships with my friends. They are not only the people that I like to spend time with, but also are essential in my growth and development as a human being. The pages in this book include insights from others just like you and me. They want to help you get through the common struggles of college with confidence and perseverance. Consider them your most recent new friends. I truly hope that this inspires you in your quest for a great future.
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CC licensed content, Shared previously:
Foundations of Academic Success: Words of Wisdom. Edited by Thomas Priester. Essay authored by Paulo Fernandes. Located at: https://milnepublishing.geneseo.edu/...om-my-friends/ License: CC BY: Attribution.


MO Theory: Simplest Examples
Skills to Develop
- Construct MO diagrams for H 2 and He 2
- Define bond order in theory and calculation
MO Theory for H 2
Let's find the MO description of H 2 . We are going to use one electron on each H atom, each in a 1s orbital. When we bring the 2 atoms next to each other, we can make 2 MOs out of the 2 1s AOs. As always, we will do a + combination and a — combination. These combinations are illustrated in the figure below.
Notice that the + combination produces an MO with more electron density between the nuclei, because the waves interfere constructively. The — combination produces an MO with a node between the nuclei, and not much electron density there, because the waves interfere destructively. If you think about the Coulomb's law forces, and imagine putting 2 electrons in the + MO, they will usually be between the nuclei, and the attractions between the electrons and nuclei will hold the nuclei together, making the molecule. For this reason, the + MO is called a bonding MO . On the other hand, if we imagine putting 2 electrons in the — MO, they will usually be on the outside of the nuclei, so the repulsion between the nuclei will push them apart, and no molecule will form. For this reason, the — MO is called an anti-bonding MO .
You've seen before that more nodes means higher energy.  So it makes sense that the bonding MO (no nodes) is lower in energy than the anti-bonding MO (1 node). Thus, in H 2 , both electrons will go in the bonding MO, and the molecule is stable. In fact, the bonding orbital will be lower in energy than the AOs it was made from, because of the increased Coulomb attractions. The anti-bonding orbital will be higher in energy than the AOs because of the increased Coulomb repulsions. We can represent this with an MO diagram, shown in the figure.
MO Theory for He 2
Now let's think about He 2 . We still have a combination of 2 AOs, both 1s. The bonding and anti-bonding orbitals will look very similar. But now we have 4 electrons, so we will have to put 2 electrons in each MO. Because the molecule He 2 does not exist, we can conclude that the anti-bonding orbital increases in energy more than the bonding orbital decreases in energy, so that He 2 is higher energy than 2 He.
Bond Order in MO Theory
One great thing about MO theory is that it makes it really simple to think about partial bonds and weird molecules, like radicals. The table shows some data for a few examples.
| Molecule |
Bond Length
(Å) |
Bond energy
(kcal/mol) |
|---|---|---|
| He 2 | * | * |
| H 2 + | 1.06 | 61 |
| He 2 + | 1.08 | 55 |
| H 2 | 0.74 | 103 |
Now try drawing the MO diagram for each molecule. What do you notice? If we calculate
net bonding electrons = (number of bonding electrons) — (number of anti-bonding electrons)
we get:
| Molecule |
Bonding
Electrons |
Anti-Bonding
Electrons |
Net Bonding
Electrons |
Bond Length
(Å) |
Bond energy
(kcal/mol) |
|---|---|---|---|---|---|
| He 2 | 2 | 2 | 0 | * | * |
| H 2 + | 1 | 0 | 1 | 1.06 | 61 |
| He 2 + | 2 | 1 | 1 | 1.08 | 55 |
| H 2 | 2 | 0 | 2 | 0.74 | 103 |
The number of net bonding electrons predicts the length and strength of the bond! Since we normally think of a chemical bond as a 2-electron bond, we can define the bond order like this:
\[Bond\; Order = \frac{\left(bonding\; e^{-}\right) - \left(anti \mbox{-} bonding\; e^{-}\right)}{2}\]
If bond order = 1, there is a single bond (H 2 , for instance). If bond order = 0, we expect no bond. If bond order = 0.5, we have a 1-electron bond or a half bond. It's approximately half as strong as a 2-electron bond.


8.3: Part 1- Nature Walk Observations instructions
Going on a nature walk is a great opportunity to apply your knowledge and skills in a real-world setting.
Look at a map of your campus to identify the trail to be taken and identify potential areas of interest before you set foot outside.
OR
Choose a location : Pick a park, nature trail, or other natural area that you want to explore. Make sure the location is safe and suitable for the type of observations you want to make.
- Gather your supplies: You will need a notebook, pen or pencil, thermometer, hand lens (or other magnifying device), and a camera or smartphone to take pictures of what you observe. You can also bring a field guide or app (such as Seek or Google Lens) to help identify plants and animals.
- Start your walk: As you walk, look around and pay attention to the various plants, fungi, and animals in the area. Make note of the different types of vegetation and their growth patterns, as well as the different species of animals and their behaviors.
- Make observations: Record your observations in your notebook, including descriptions of the physical characteristics of the plants and animals, as well as their behaviors and interactions with each other. Also, take pictures of anything interesting that you want to remember. You can insert these pictures into your notebook later.
- Identify what you observe: Use a field guide or app to identify the plants and animals you see. Write down the names of the species you observe in your notebook, along with any other relevant information such as their classification and habitat.
- Look for patterns: Look for patterns in your observations, such as the relationship between the types of vegetation and the species of animals present. Consider how the environment affects the habitat, behavior, and interactions of plants and animals.
- Make hypotheses: Based on your observations, formulate hypotheses about the relationships between the different components of the ecosystem and how they may be affected by environmental factors such as temperature, rainfall, and light.
- Analyze your data: After your nature walk, analyze your data and draw conclusions based on your observations and hypotheses. Consider how your findings relate to the larger scientific community's understanding of the ecosystem and its components.
- Present your findings (optional): Present your findings to your classmates or submit a report to your teacher. Discuss the implications of your observations for the broader understanding of the ecosystem and the environment.
Activities for after the walk
Draw a food web including organisms that you saw in the same area, interacting together. Make sure to include a producer , at least two levels of consumers , and a decomposer . Label which organisms are autotrophs and which are heterotrophs . Use arrows to show how energy is transferred and lost throughout this web.
Figure 1. Example food web (CCBY 4.0 Kestin Schulz, Mariya W. Smit, Lydie Herfort and Holly M. Simon. The image (amended) was provided courtesy of the Missouri Department of Conservation.)
Food web drawing . Try to draw this somewhat as you saw it. For example, trees rooted in soil, bug on a leaf that is attached to grass, fungus growing from the ground, etc. Draw black arrows from the thing that might be eaten to the thing doing the eating.
What is the ultimate source of energy for your food web?
What happens to this energy as it moves through the food web? Where does it end up?
In drawing your food web, you depicted a combination of the flow of energy and the cycling of nutrients through an ecosystem. Whereas energy has an input and an output, nutrients are continually recycled. These elements often cycle between the biotic and abiotic components in an ecosystem.
For example, water is composed of hydrogen and oxygen atoms. Water molecules precipitate from the atmosphere and fall as rain, saturating the soil. A plant absorbs those molecules through its roots, transporting them up to its leaves. Some of these water molecules will be broken apart during the process of photosynthesis, the oxygen exiting the plant as O2.
O2 is gas that you will breathe in, while the hydrogen removed from the water might be used to form molecules of glucose that you will eat. The water not being broken apart exits the plant through its leaves, evaporating back into the atmosphere in a process called transpiration . The oxygen atoms that you breathed in will be used to release energy from your food ( cellular respiration ) and be joined back to hydrogen molecules to once again form water. This water might exit your body as vapor on your breath or as perspiration and return directly to the atmosphere. It might also soak into your clothes as sweat or exit as urine, be processed in a wastewater facility, then sent out to the ocean where it will evaporate back into the atmosphere.
Oxygen and carbon cycles through different processes. (CCBY 4.0 Wikimedia Commons as a contribution from an Art&Design School thanks of a collaboration between Llotja and A mical Wikimedia .)
The atoms of hydrogen and oxygen are broken apart and reassembled into other molecules multiple times in this process, but the overall outcome is a cycle, with atoms traveling between the atmosphere, hydrosphere, lithosphere, and biosphere , but rarely ever exiting our Earth system.
Using a blue pen or pencil, diagram the flow of water through the ecosystem around you in the food web you drew.
What is the role of plants in the global cycling of water?
Each species in an ecosystem is considered a population . This represents a group of actually or potentially interbreeding organisms and is an important area of study for both ecologists and geneticists. When multiple species in an ecosystem are considered together, this is called a community . For example, a forest could be composed of a single population of maple trees, but it is more likely to be a community, including other tree species like oak and pine, and animals like the whitetail deer or rainbow trout. All living organisms are considered to be a part of the community in a given ecosystem.
What is the difference between a community and an ecosystem?


3.5: The Future
With the data that have been gathered over the past 50-100 years on temperature, precipitation, ice melt, sea levels, and other factors related to climatic change, scientists can build models to represent the patterns that we have observed already and use these models to extrapolate predictions for what can be expected to occur in the near future. Frequently, scientists use multiple possible future scenarios, called Representative Concentration Pathways (RCPs) which are based on different choices that humans may make in the future and how these decisions affect future climatic change. RCPs differ primarily in the time period at which global GHG emissions peak and begin to decline and therefore how much warming we can expect. The commonly used RCPs are defined below:
- RCP 2.6: global annual GHG emissions peak 2010-2020
- RCP 4.5: global annual GHG emissions peak around 2040
- RCP 6.0: global annual GHG emissions peak around 2080
- RCP 8.5: global annual GHG emissions continue at their current level through the year 2100
Each RCP is named with a number that represents the difference in sunlight absorbed by the Earth’s surface versus sunlight reflected back to space (discussed in Fig 3.1.1). Larger numbers represent a larger increase in absorption of sunlight and, therefore, more warming. The ‘best case scenario’, RCP 2.6, requires a peak-and-decline of global GHG emissions to occur by 2020; consequently, the best case scenario is no longer possible. The most extreme scenario currently used in the projections, RCP 8.5, assumes no major declines in GHG emissions until after the year 2100. This scenario is commonly referred to as ‘business as usual.’ Given the lack of binding international agreements which would limit or reduce future global GHG emissions, we are currently following RCP 8.5. Scientists can use the different RCPs to consider the impact of different global political decision making. As seen in Figure 3.5.1, the differences can be profound. These decisions matter, and the longer we as a global community take to respond to the threats of climate change and alter our GHG emissions, the more severe the ramifications will be.


2.5: Processes and Paths
A process is a change in the state of the system over time, starting with a definite initial state and ending with a definite final state. The process is defined by a path , which is the continuous sequence of consecutive states through which the system passes, including the initial state, the intermediate states, and the final state. The process has a direction along the path. The path could be described by a curve in an \(N\)-dimensional space in which each coordinate axis represents one of the \(N\) independent variables.
This e-book takes the view that a thermodynamic process is defined by what happens within the system, in the three-dimensional region up to and including the boundary, and by the forces exerted on the system by the surroundings and any external field. Conditions and changes in the surroundings are not part of the process except insofar as they affect these forces. For example, consider a process in which the system temperature decreases from \(300\K\) to \(273\K\). We could accomplish this temperature change by placing the system in thermal contact with either a refrigerated thermostat bath or a mixture of ice and water. The process is the same in both cases, but the surroundings are different.
Expansion is a process in which the system volume increases; in compression , the volume decreases.
Figure 2.9 Paths of three processes of a closed ideal-gas system with \(p\) and \(V\) as the independent variables. (a) Isothermal expansion. (b) Isobaric expansion. (c) Isochoric pressure reduction.
Paths for these processes of an ideal gas are shown in Fig. 2.9. An isothermal process is one in which the temperature of the system remains uniform and constant. An isobaric or isopiestic process refers to uniform constant pressure, and an isochoric process refers to constant volume.
An adiabatic process is one in which there is no heat transfer across any portion of the boundary. We may ensure that a process is adiabatic either by using an adiabatic boundary or, if the boundary is diathermal, by continuously adjusting the external temperature to eliminate a temperature gradient at the boundary.
Recall that a state function is a property whose value at each instant depends only on the state of the system at that instant. The finite change of a state function \(X\) in a process is written \(\Del X\). The notation \(\Del X\) always has the meaning \(X_2 - X_1\), where \(X_1\) is the value in the initial state and \(X_2\) is the value in the final state. Therefore, the value of \(\Del X\) depends only on the values of \(X_1\) and \(X_2\). The change of a state function during a process depends only on the initial and final states of the system, not on the path of the process.
An infinitesimal change of the state function \(X\) is written \(\dif X\). The mathematical operation of summing an infinite number of infinitesimal changes is integration, and the sum is an integral (see the brief calculus review in Appendix E). The sum of the infinitesimal changes of \(X\) along a path is a definite integral equal to \(\Del X\): \begin{equation} \int_{X_1}^{X_2} \!\dif X = X_2-X_1 = \Delta X \tag{2.5.1} \end{equation} If \(\dif X\) obeys this relation—that is, if its integral for given limits has the same value regardless of the path—it is called an exact differential . The differential of a state function is always an exact differential.
A cyclic process is a process in which the state of the system changes and then returns to the initial state. In this case the integral of \(\dif X\) is written with a cyclic integral sign: \(\oint \dif X\). Since a state function \(X\) has the same initial and final values in a cyclic process, \(X_2\) is equal to \(X_1\) and the cyclic integral of \(\dif X\) is zero: \begin{equation} \oint \dif X = 0 \tag{2.5.2} \end{equation}
Heat (\(q\)) and work (\(w\)) are examples of quantities that are not state functions. They are not even properties of the system; instead they are quantities of energy transferred across the boundary over a period of time. It would therefore be incorrect to write “\(\Del q\)” or “\(\Del w\).” Instead, the values of \(q\) and \(w\) depend in general on the path and are called path functions .
This e-book uses the symbol \(\dBar\) (the letter “d” with a bar through the stem) for an infinitesimal quantity of a path function. Thus, \(\dq\) and \(\dw\) are infinitesimal quantities of heat and work. The sum of many infinitesimal quantities of a path function is not the difference of two values of the path function; instead, the sum is the net quantity: \begin{equation} \int \! \dq = q \qquad \int \! \dw = w \tag{2.5.3} \end{equation} The infinitesimal quantities \(\dq\) and \(\dw\), because the values of their integrals depend on the path, are inexact differentials .Chemical thermodynamicists often write these quantities as \(\dif q\) and \(\dif w\). Mathematicians, however, frown on using the same notation for inexact and exact differentials. Other notations sometimes used to indicate that heat and work are path functions are \(\tx{D}q\) and \(\tx{D}w\), and also \(\delta q\) and \(\delta w\).
There is a fundamental difference between a state function (such as temperature or volume) and a path function (such as heat or work): The value of a state function refers to one instant of time; the value of a path function refers to an interval of time .
The difference between a state function and a path function in thermodynamics is analogous to the difference between elevation and trail length in hiking up a mountain. Suppose a trailhead at the base of the mountain has several trails to the summit. The hiker at each instant is at a definite elevation above sea level. During a climb from the trailhead to the summit, the hiker’s change of elevation is independent of the trail used, but the trail length from base to summit depends on the trail.


6.1.2: How Does Having a Developmental Disability Affect Normal Development?
Having a developmental disability can affect normal development in a variety of ways. It all depends on the type of developmental disability the person has.
Self-Care & Movement
The person may have trouble performing activities of daily living (ADLs) independently. They may be unable to perform tasks such as bathing, dressing, toileting, or feeding themselves. If the developmental disability impacts their physical functioning, the person may have trouble using their muscles. They may for example, be unable to control their muscle movements. This may affect their ability to perform ADLs, to walk, and to get from one place to another.
Communication & Social Situations
‘The person with a developmental disability may have trouble communicating with others. They may have difficulties with speaking, understanding the speech of others, writing, or reading. The person may have trouble in social situations. In addition to communication problems, they may have difficulties understanding social situations. They may have trouble understanding social cues and things such as nonverbal communication. This can be a source of great frustration for the person with a developmental disability. Having difficulties communicating with others can impact their ability to make friends and have the social support they need. This may also impact their ability to perform in school, work, and in social settings.
Financial Independence & Self-Direction
The difficulty or inability to perform in a setting such as a work setting can affect a person’s ability to provide for themselves and support themselves financially. This impacts the person’s ability to live independently. They may need to rely on others to care for them for their entire lives. If a person needs to depend on others to care for them, they may feel an inability to make choices for themselves and to control the direction of their own lives.
Coping
The person’s ability to cope with stressors may also be impacted. If a person has difficulties physically performing tasks, moving, communicating with others, being understood, supporting themselves physically and financially, they may have many different emotions. They may feel angry, frustrated, resentful, depressed, hopeless, guilty, and even embarrassed. They may also have a hard time letting others know their needs, wants, and feelings.
Families with a person with a developmental disability may also have a difficult time coping. They too may feel angry, frustrated, resentful, depressed, hopeless, guilty, and even embarrassed. Home Health Aides/Personal Care Aides can help provide the emotional support the patient and family needs in addition to providing assistance with physical tasks such as feeding and dressing.


3.1.4: Paper- Popular Culture is Only Useful as a Text for Criticism
Author: Mark D. Pepper, English, Utah Valley University
Popular culture, once written off as lacking depth and importance, is now the subject of in-depth analysis both on college campuses and in non-academic venues. Students write extended considerations of how cult TV show Buffy the Vampire Slayer explores teen insecurities through their embodiment in the show’s demonic villains. Bookstores sell essay collections with titles like Myth, Media, and Culture in Star Wars and The Sopranos and Philosophy . Online think pieces analyze how Taylor Swift’s lyrics may or may not be feminist. A public wiki devoted to the television show LOST still has devoted fans trying to figure out what it all meant (maybe even figuring out what those accursed numbers were all about).
All this writing increasingly problematizes the argument that popular culture is primarily dumb, simplified fodder for the masses. In his book, Everything Bad is Good For You , Steven Johnson builds a sustained argument that popular culture (especially in the past three decades) has become more complex, better written, and cognitively stimulating. The existence of so many college courses, mass-marketed books, and online pieces of analysis suggest that popular culture warrants close textual scrutiny. The popularity of this writing also suggests a desire for consumers to dig deeper into what their entertainment is about and what broader cultural effects it may have. Considering the actual depth of pop culture texts, it’s not surprising that performing deep reading is so popular in the classroom.
This textual analysis of popular culture for its deeper meanings or cultural effects is not a bad idea in and of itself; in fact, getting popular culture taken seriously was a hard-fought struggle in academic circles throughout the latter half of the 20th century. However, that battle was seemingly won on the idea that popular-culture texts should be treated in the same manner as classic literature where textual features such as symbolic and metaphorical messages are treated as important elements of the texts. Therein lies the problem. When popular culture is predominantly written about from the perspectives of textual analysis and cultural criticism, this writing often fails to capture the personal, varied, and complex experiences of consuming popular culture. Students often balk at these writing assignments because they recognize that something is missing (or murdered, in the words of William Wordsworth). Without different kinds of writing assignments that balance the rush to critique content, students are seemingly asked to disregard a lifetime of experience with these texts that do not seem valued by an educational setting that is laser focused on textual dissection.
The Unique Place of Popular Culture in Daily Life
When popular culture is brought into a classroom as analytical fodder for student papers, the results are often smart and well written. Such writing often presents the popular text in a “here’s its deeper meaning” light, sometimes to counter the still-common misconception that pop culture is lower or dumber than other forms of texts. Other written analysis often suggests how a popular text is damaging because of the problematic representations of society’s marginalized and disenfranchised groups through encoded, normalized messages and symbols. And the assignments work. Students writing in this vein hit all the checkboxes currently heralded by educational goals and outcomes statements: critical thinking, inquiry, close reading, and working with diverse texts. However, saying this type of writing works means something very specific and potentially limiting.
When instructors ask students to write about Buffy the Vampire Slayer or Breaking Bad with the same focal points also applied to Hamlet or Moby-Dick , there’s an implied message that pop culture is not more than that. Sure, the texts may operate similarly in some ways (they all have symbolically charged, complex plots, characters, and themes), however, the popular texts operate in some uniquely different ways too. These are the texts we get hyped for and binge in encaptivating doses. These are the texts that inspire us to buy related t-shirts, toys, and memorabilia. These are the texts we avoid spoilers for and geek out with our friends about (sometimes while wearing costumes of characters from the text). These are the texts sometimes so bad that we watch them simply because they are so bad (hey, Sharknado) . These are the texts that are sometimes just on or just there—a background tapestry for everyday living. Pop culture is a unique and contradictory site of meaning making that often (and usually) goes far beyond the definition of meaningfulness required by a textual analysis/critique writing assignment. It’s a realm of personal connections, emotional nuance, and messy contradictions that defies most traditional grading rubrics.
This is not to suggest that literature (or even essays) offered for analysis in the classroom don’t also come with personal connections, entertainment value, and emotional perspectives. However, standard-issue writing assignments far too often ask that those factors be stripped away or ignored in the actual writing (some instructors of writing still inexplicably discourage the use of “I” in any situation). So it’s not hard to imagine how some students react negatively when they’re suddenly asked to dissect pop culture in ways that explicitly (or implicitly) ask them to disregard everything they know and feel about a popular text and reduce it to a textual artifact for parsing.
Textual analysis often come with an implied demand for the readers of such pieces to reject their enjoyment (or, at least, feel guilty about it), and adopt the correct stance when a problematic element is being dissected. Fans may rightly ask: Why should this author’s critical interpretation affect my personal relationship with the text just because he or she has a degree or book contract? Another response may be: I see now that this text is problematic, but I still like it. After all, close textual analysis might change minds (or add some nuance) for some readers and writers, but it more likely allows readers who already have these specific critical tendencies to feel good about being on the right side of what they already know.
Here, the unique status of popular culture must be noted again. Students likely expect that the authors of critical essays about Toni Morrison or Kafka know more about the texts than they do. Students often (but not always) have little prior experience with the work. And students write cautiously and with reservation about Beloved or The Metamorphosis because they’re treading new ground. But when pop culture becomes the topic of writing, students may have the feeling that something is missing because they bring so much prior experience with them to the blank page. They have a knowledge base from which to confidently observe, “Well, that hasn’t been my experience with the text.” Not to be misunderstood, it’s obviously good to encounter new perspectives and question previous assumptions. Nonetheless, the question becomes: What is being taught about writing when textual/critical analysis asks students to disregard their outside expertise, turn off their personal investments, and attack (from their points of view) texts that they know are more complex than narrative meaning and cognitive impact?
Fandom Studies and Affective Musings
Again, the problem is one of ratio. These textual/critical analyses wouldn’t be so potentially limiting if they were more frequently balanced with other ways of writing about popular culture. One alternate direction is summed up under the loose banner of fandom studies.
In fandom studies, textual critique takes a backseat to observing how texts are reacted to, invested in, and made part of fans’ identities and daily lives. While textual critique often assumes a text’s particular effects, fandom studies goes to the source and lets fans and their practices speak for themselves (though still filtered through the critical lens of the observer). Fandom writing also brings a myriad of possibilities to the classroom. Students can write ethnographic research reports on face-to-face or digital communities that chart the movement of writing practices within a network of fan activity. Fan fiction can be analyzed (and even compared to the original work) as an exercise in learning style and voice. The clever and surprising alterations in fan fiction also have much to teach about creativity and invention. Finally, fandom offers avenues to analyze or produce transliteracy —the process of writing across different media with a variety of tools. For example, The Lizzie Bennet Diaries is a popular YouTube channel that video blogs (vlogs) the modernized lives of characters from Pride and Prejudice . Along with the vlogs, the characters use Twitter and Google+, which allows fans to co-create and shape the ongoing story.
Popular culture may also be written about in ways that go beyond the confines of textual content. Lawrence Grossberg argues that outside the actual content being considered, the pleasure people take in popular culture, is primarily based in affective investments. Affect (admittedly a complex concept too broad for full exploration here) can aptly be understood as the motivating force that adds intensity to our daily interactions and subsequently leads to an individual’s sense of what matters—the feeling of life. Obviously, textual and ideological content sometimes matter in our enjoyment or dislike of a text; however, they are just two pieces of the puzzle because affect privileges the depth and complexity of feeling over textual meaning. Grossberg suggests that our encounters with popular texts are intensified (or come to matter) by the complex investments of emotion, passion, mood, and energy that we bring to them in the process of actively integrating popular texts into our identities and social lives. This is the element of popular culture consumption missed in a million close, textual readings. This is where textual meaning is merely a starting place for a text’s integration into a person’s identity and social performance.
So what does affective popular culture writing look like? Such writing is less concerned with criticism and more focused on what the text means to the author’s life. The writing is more personally revealing and socially inviting as it attempts to chart the author’s investment in a text, while simultaneously inviting the audience to recognize themselves and reflect on their own relationship to the subject matter. Put differently, affective writing shows authors speaking directly for the texts that usually speak for them. The work of Chuck Klosterman, a pop culture essayist, provides an apt example. Though Klosterman does not avoid textual criticism and cultural effect (as in his essay critiquing how MTV’s The Real World created “one-dimensional personalities”), he consistently connects pop culture to his personal experiences in a memoir-like style. Whether he’s writing an ode to the universality of Billy Joel, analyzing how porn feeds our need for amateur celebrities, noting how people dismiss country music to sound cool, or what he learned from extensively playing The Sims video game, Klosterman’s work highlights how popular culture makes us feel, makes us connect, and makes us discuss.
Embracing affect leads to a more personal style of student writing about pop culture but does not have to lead to completely subjective journaling (not that there’s anything wrong with that either). Though students are encouraged to write about their participation and engagement with popular culture, the focus is more on the intensity and complexity of that enjoyment. Pleasure (and distaste) is a complicated orientation that, from an affective perspective, is created by any number of extratextual features: early memories of the text (or its genre), opinions about the texts’ fans, how the text is publically disseminated, public images/narratives of the artist, and ways the text encourages social investment. By the nature of affect, some of these aspects will necessarily matter more or less. As student writings map this complex web of personal/ social investments (intensely engaging with some while possibly ignoring others), the writer understands that textual effects and reactions (plus the motivations texts may or may not spur) are often unpredictable, contradictory, and incomplete. Such a lesson is fundamentally important when a purely textual focus often implicitly teaches that writing has a unified effect and preferred interpretation.
Textual/critical analysis certainly has an important place. However, as the dominant form of writing about popular culture, it often fails to account for the ways pop culture is used when the viewer isn’t specifically focused on critique. Pop culture is a complex space that creates diverse, contradictory, and messy ways to consume, participate, identify, discuss, and make meaning. And pop culture is too entrenched in the daily lives of millions to let one type of writing oversell its importance. Through balancing pop culture use in the classroom, students continue to learn analytical criticism while simultaneously being awarded for their current expertise and complex relationships with the source material.
Further Reading
For more information on the history of popular culture analysis and criticism, see Culture, Media, Language (Routledge), which charts the theories and methodologies of The Centre for Contemporary Cultural Studies throughout the 1970s. Though obviously not the only group of thinkers to influence how pop culture became a subject for textual criticism, many of the school’s members and writings form important historical touchstones for the type of analysis critiqued in this chapter. The book includes Stuart Hall’s (director of the Centre from 1974–1979) famous work, “Encoding/ Decoding,” which highlights how cultural producers create and distribute ideology and meanings through texts that readers can either accept/naturalize or critique/resist.
For more on the theories and methods of fandom studies, Henry Jenkins is arguably the most well-known name in what is often a diverse field. His books, T extual Poachers: Television Fans and Participatory Culture (Routledge) and Fans, Bloggers, and Gamers: Media Consumers in a Digital Age (NYU Press), both allow textual criticism to take a backseat to the practices and dispositions of fans. For a broader take on fandom studies as a whole, Mark Duffett’s (Bloomsbury) explores fan stereotypes, representations, and practices while citing many thinkers in the field along the way. His chapter, “Beyond the Text” is most applicable to this chapter, in that, it explores how criticism and analysis alone will always miss out on the lived experience of the text under scrutiny.
As this chapter mentions, affect theory is complex and really needs a fuller study to appreciate both its usefulness and limitations. Lawrence Grossberg’s Bringing it All Back Home: Essays on Cultural Studies (Duke University Press) collects some of his earliest writings on the relationship between affect and pop culture consumption and enjoyment. But for a more current take on competing definitions and applications of affect theory, Melissa Gregg and Gregory J. Seigworth’s collection, The Affect Theory Reader (Duke University Press), probes much deeper into the nuances and ramifications of this pre-conscious, intensity producing force that shapes our attachments and affinities for popular culture’s offerings.
Keywords
affect, cultural studies, fandom, popular culture, taste studies
Author Bio
Mark D. Pepper is an associate professor of English at Utah Valley University where he teaches courses in composition, technical writing, popular culture, and graphic novels. Much of his research deals with how people use and talk about popular culture in their daily lives to create both personal identity and social belonging. His dissertation looked at how the popularity of texts is created and spread in a digital age of blogs, wikis, and social media. His own pop culture fandom started with comic books as a kid and carries on to a Netflix queue full of television series with far too many seasons to ever reasonably catch up on.


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autonomous interdependence
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according to Selman, adult stage of friendship in which friends appreciate and respect each other’s individuality and identity while also relying on each other for the support
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homogamy
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preference for forming romantic relationships with those who are similar to us
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intergenerational solidarity
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closeness among family generations promoted by frequent interaction, expressions of affection, alignment of values and beliefs, provision of help, proximity to each other, and shared norms and traditions
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intersectionality
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framework to understand how people experience multiple aspects of their identity simultaneously
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intimacy vs. isolation
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according to Erikson’s theory of psychosocial development, the early adulthood challenge to establish close and trusting relationships with others
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maturity principle of personality development
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increase or decrease of certain traits with age to effectively adapt to the demands of development
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mean-level change
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extent to which the level of a personality trait can fluctuate historically and over the lifespan
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rank-order stability
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tendency for an individual’s levels of personality traits compared to others to remain stable over time
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self
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totality of all your personal characteristics, including the way you see yourself, represent yourself, and relate to others
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self-determination theory
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theory that proposes that success and well-being are maximized when we are able to balance our needs for autonomy, competence, and relatedness
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social clock
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cultural expectations about normative behavior and achievements that are associated with age
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social investment theory of personality development
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idea that commitment to certain life roles predicts corresponding changes in personality traits to support the demands of these roles
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trajectory
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predicted pathway of development, usually determined by the interaction of behaviors within context
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work-life balance
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arrangement that allows a person to spend the desired amount of time on activities that are important to them such as work, leisure, education, and caregiving


12.5.2: Procedure- Assisting with the Use of Elastic Support Stockings
Some patients may be prescribed by their doctor special elastic support stockings or compression stockings to wear on their legs. These stockings are used for patients with poor circulation who are at risk for getting a blood clot. They are also used to help prevent or reduce swelling. Stockings should be placed on the patient’s legs prior to them getting out of bed in the morning. Follow manufacturer instructions in applying stockings. Follow instructions written in the Care Plan for guidelines for when to apply, how long the patient should wear stockings each day, and when to remove stockings.
- Explain the procedure to the patient. Ensure they understand the importance of wearing the elastic support stockings. Seek guidance from a supervisor as needed and report refusal to wear stockings.
- Wash and dry your hands.
- Assemble equipment (e.g. support stockings, lotion, shoes).
- If the patient has been moving around out of bed, have them lie down with their legs elevated for 15 minutes before applying the stockings.
- Make sure legs are clean and dry. Observe skin for condition and changes such as sores, swelling, and changes in color. Make note of any observed changes and any patient complaints such as numbness, pain, or tingling in the lower extremities.
- You may use powder or lotion on the patient’s legs prior to applying the stockings. This provides for comfort, ease of application of stockings, and protection for the patient’s skin.
- Raise the bed to waist height. Position patient in the supine (lying on back) position.
- Apply stockings according to the Care Plan and as a supervisor directs.
- Place your hand and arm inside one stocking and turn it inside out up to the heel of the stocking. Grasp the heel of the stocking with your fingers of the hand holding the stocking.
- Move the stocking down over your arm so that the length of the stocking is now bunched near your hand.
- Carefully take the patient’s foot and position the opening of the stocking that is near your hand over the patient’s toes.
- Place the foot of the stocking over patient’s toes, then over the foot, then over the heel. Pull the stocking up slowly as you move it upwards over the patient’s leg.
- Gently pull the top of the stocking up over the entire calf.
- Make sure the heel of the foot is in the heel of the stocking.
- If there are no toe openings, gently pull on the tip of the stocking by the toes to relieve pressure. For stockings with toe openings, the patient’s toes should be positioned appropriately in the toe area.
- Repeat with the other leg.
- Always ensure there are no wrinkles in the stockings.
- Discard gloves if wearing and wash your hands.
- If the stockings do not appear to fit well and appear to be digging into the top of the patient’s leg, inform a supervisor right away. The patient may need to be refitted for the appropriate sized stocking.
- Stockings should be removed and skin should be cleaned, dried, and inspected at least once per day.
- Observe for changes in skin color, temperature, swelling, sores on legs, and patient complaints.
- Document and report any changes in condition or behavior.


8.1: Introduction to Confidence Intervals
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Suppose you were trying to determine the mean rent of a two-bedroom apartment in your town. You might look in the classified section of the newspaper, write down several rents listed, and average them together. You would have obtained a point estimate of the true mean. If you are trying to determine the percentage of times you make a basket when shooting a basketball, you might count the number of shots you make and divide that by the number of shots you attempted. In this case, you would have obtained a point estimate for the true proportion the parameter \(p\) in the binomial probability density function.
We use sample data to make generalizations about an unknown population. This part of statistics is called inferential statistics . The sample data help us to make an estimate of a population parameter . We realize that the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals. What statistics provides us beyond a simple average, or point estimate, is an estimate to which we can attach a measure of accuracy, what we will call a confidence level. We make inferences with a known level of confidence.
In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's- t , and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable (until a specifi interval is calculated). It is the population parameter that is fixed.
If you worked in the marketing department of an entertainment company, you might be interested in the mean number of songs a consumer downloads a month from iTunes. If so, you could conduct a survey and calculate the sample mean, \(\overline x\), and the sample standard deviation, \(s\). You would use \(\overline x\) to estimate the population mean and \(s\) to estimate the population standard deviation. The sample mean, \(\overline x\), is the point estimate for the population mean, \(\mu\). The sample standard deviation, \(s\), is the point estimate for the population standard deviation, \(\sigma\).
\(\overline x\) and \(s\) are each called a statistic .
A confidence interval is another type of estimate but, instead of being just one number, it is an interval of numbers. The interval of numbers is a range of values calculated from a given set of sample data. The confidence interval is likely to include the unknown population parameter.
Suppose, for the iTunes example, we do not know the population mean \(\mu\), but we do know that the population standard deviation is \(\sigma = 1\) and our sample size is 100. Then, by the Central Limit Theorem, the standard deviation of the sampling distribution of the sample means is
\[\frac{\sigma}{\sqrt{n}}=\frac{1}{\sqrt{100}}=0.1.\nonumber\]
The Empirical Rule , which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population mean \(\mu\). For our iTunes example, two standard deviations is \((2)(0.1) = 0.2\). The sample mean \(\overline x\) is likely to be within 0.2 units of \(\mu\).
Because \(\overline x\) is within 0.2 units of \(\mu\), which is unknown, then \(\mu\) is likely to be within 0.2 units of \(\overline x\) with 95% probability. The population mean \(\mu\) is contained in an interval whose lower number is calculated by taking the sample mean and subtracting two standard deviations \((2)(0.1)\) and whose upper number is calculated by taking the sample mean and adding two standard deviations. In other words, \(\mu\) is between \(\overline{x}-0.2\) and \(\overline{x}+0.2\) in 95% of all the samples.
For the iTunes example, suppose that a sample produced a sample mean \(\overline{x}=2\). Then with 95% confidence the unknown population mean \(\mu\) is between
\[\overline{x}-0.2=2-0.2=1.8 \text { and } \overline{x}+0.2=2+0.2=2.2 \nonumber\]
We say that we are 95% confident that the unknown population mean number of songs downloaded from iTunes per month is between 1.8 and 2.2. The 95% confidence interval is (1.8, 2.2). Please note that we talked in terms of 95% confidence using the Empirical Rule. The Empirical Rule for two standard deviations is only approximately 95% of the probability under the normal distribution. To be precise, two standard deviations under a normal distribution is actually 95.44% of the probability. To calculate the exact 95% confidence level we would use 1.96 standard deviations.
The 95% confidence interval implies two possibilities. Either the interval (1.8, 2.2) contains the true mean \(\mu\), or our sample produced an \(\overline x\) that is not within 0.2 units of the true mean \(\mu\). The second possibility happens for only 5% of all the samples (100% minus 95% = 5%).
Remember that a confidence interval is created for an unknown population parameter like the population mean, \(\mu\).
For the confidence interval for a mean the formula would be:
\[\mu=\overline{X} \pm z_{\alpha/2} \sigma / \sqrt{n}\nonumber\]
Or written another way as:
\[\overline{X}-z_{\alpha/2} \frac{\sigma}{{\sqrt{n}} \leq \mu \leq \overline{X}+z_{\alpha/2} \frac{\sigma}{\sqrt{n}}\nonumber\]
Where \(\overline X\) is the sample mean. The critical value , \(z_{\alpha/2}\), is determined by the level of confidence desired by the analyst, and \(\sigma / \sqrt{n}\) is the standard deviation of the sampling distribution for means given to us by the Central Limit Theorem.


Several factors have recently converged to propel learning applications for computer-based games.
Popularity and Access
First, games are widely popular and accessible as entertainment; the Canadian video game market will increase from $732 million in 2005 to $1.3 billion in 2010, while global video game spending is expected to rise from $27.1 billion in 2005 to $46.5 billion in 2010 (Forest, 2006). A 2002 US survey found that 92 percent of children and adolescents ages 2 to 17 played video games, and more than two-thirds of all children ages 2 to 18 lived in a home with a video game system (Kaiser Family Foundation 2002). As well, 61 percent of Canadian households and 75 percent of US households used mobile phones in 2005 (Wright, 2006). Using games for learning builds on their familiarity and relatively easy access.
Player Engagement
Computer games are highly engaging. Today’s games offer motivating, absorbing, interactive, collaborative experiences that draw in players and keep them playing for many hours, often developing complex social networks in the process.
A growing body of literature analyzes aspects of games that foster player engagement and motivation. Asgari and Kaufman (2004) cite three categories of factors that sustain a game’s intrinsic motivation so that a player will play for his/ her own interest and enjoyment, even in the absence of external rewards:
Table \(\PageIndex{1}\): Intrinsically Motivating Features of Games (Asgari & Kaufman, 2004)
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Feature Category
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Examples
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Psychological: those that meet individual needs
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Features that meet needs for competence, self-determination, interest-excitement, enjoyment.
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Structural: related to the inner structure of a game
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Complexity, novelty, unpredictability, uncertain outcomes, challenge, feedback, fantasy, curiosity, control, interactivity, competition
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Implementation: related to the way a game is implemented and presented to the player
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Graphics and sound, having multiple players, using well-known characters or settings, high speed, useful interface, “save game” capability
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Prensky (2001a) lists twelve elements that make computer games engaging:
Table \(\PageIndex{2}\): Twelve Elements that make Computer Games Engaging (Prensky (2001a), quoted in Mitchell & Savill-Smith, 2004)
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Game Characteristic
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Contribution to Players’ Engagement
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Fun
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Enjoyment and pleasure
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Play
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Intense and passionate involvement
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Rules
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Structure
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Goals
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Motivation
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Interaction
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Doing the activity
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Outcomes and feedback
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Learning
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Adaptive
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“Flow” state
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Winning
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Ego gratification
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Conflict/competition/ challenge and opposition
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Adrenaline
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Problem solving
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Sparks creativity
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Social interaction
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Social groups
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Representation and a story
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Emotion
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Another analysis of games’ engaging quality focuses on players’ experience of “flow”, a state of intense concentration and focus in which they have a balance between ability level and challenge, a sense of personal control over the situation, and a sense of intrinsic reward from the play (Csikszentmihalyi, 1990). Welldesigned games do this by, among other things, having multiple skills levels so that players face new but achievable challenges as they develop mastery of lower levels.
Gee (2003) explains player engagement in terms of semiotic domains (worlds of symbols, meanings, practices, and experiences). He points out that games can be very challenging and time-consuming, yet young players who might spend little time on schoolwork become absorbed in games and learn complex knowledge, responses, and behaviours in order to win. In his words,
A game like Pikmin recruits from our six-year-old a complex identity composed of various related traits. The game encourages him to think of himself as an active problem solver, one who persists in trying to solve problems even after making mistakes; one who, in fact, does not see mistakes as errors but as opportunities for reflection and learning. It encourages him to be the sort of problem solver who, rather than ritualizing the solutions to problems, leaves himself open to undoing former mastery and finding new ways to solve new problems in new situations.
Gee suggests that players take on and master lengthy, complex games because they become involved in new semiotic domains and affinity groups, resulting in new identities (e.g., a game character with abilities, faults, and decisions to be made) and situated learning that can be transferred to other domains. Squire (2005) suggests that this focus on new identities is leading to new computer-based games that build new attitudes and behaviours for players in simulated management and advertising settings.
Theory-Based Support
Computer-based games embody current learning theories. For example,
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Constructivist learning (Boethel & Dimock, 1999; Vygotsky, 1978): When requiring exploration, collaboration, and complex problem-solving, games can help players to explore, discover, articulate, and create their own understanding of complex phenomena;
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Situated cognition, cognitive apprenticeship, and experiential learning (Kolb, 1984; Schank & Neaman, 2001): When they create simulated authentic contexts and activities that involve social interaction, games can support both understanding and skill development. Also, skill development increases with learning by doing, and feedback in a safe environment;
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Self-efficacy (Bandura, 1986; Kaufman et al., 2000): Through learner control and increasing achievement levels, games can provide opportunities for successful experiences to help develop self-efficacy and positive attitudes concurrently with knowledge and skills.
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Learner-cent-redness (McCombs and Whistler, 1997): Games can transform traditional teacher and learner roles so that learners shift from a passive to an active role, and from learner to teacher through active exploration, experimentation, discovery, and collaboration with peers.
Evidence of Learning Outcomes
A number of studies have demonstrated the effectiveness of games for cognitive, emotional and psychomotor learning. For examples, see Baranowski et al. (2003), Kirriemuir & McFarlane (2004), Lieberman (2001), Roubidoux (2002), Sauvé et al. (2005b), and Steinman & Blastos (2002). According to these, games motivate learning, offer immediate feedback, consolidate knowledge, support skills development and application, aid learning transfer, and influence changes in behaviour and attitudes, all pointing to greater learning effectiveness with simulations and games.
New-Generation Learning Model
Finally, some observers argue that new generations of learners are developing new cognitive processes and a culture that is changing the nature of learning. Learning may be evolving into a much more “unruly,” less controlled process than we have been accustomed to in our classrooms (Seely Brown, 2002). Prensky (2001a) and others suggest that the “game generation” has developed a new cognitive style characterized by multitasking, a short attention span, and learning through exploration and discovery; today’s games provide their ideal learning environment.
Example \(\PageIndex{1}\)
Case studies of Lineage (Steinkuehler, 2004) and World of Warcraft (Lau, 2005) describes how these MMOGs develop online communities of practice that foster learning as social practice through “situated understandings, effective social practices, powerful identities, shared values, and shared ways of thinking” (quote from Lau, 2005).


8.13: Proficiency Exam
Proficiency Exam
Find the domain of \(\dfrac{5a + 1}{a^2 - 5a - 24}\)
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\(a≠−3,8\)
For the following problems, fill in the missing term.
\(-\dfrac{3}{x+4} = \dfrac{?}{x + 4}\)
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\(−3\)
\(\dfrac{2x + 5}{-x + 1} = \dfrac{?}{x - 1}\)
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\(−2x−5\)
For the following problems, reduce to lowest terms.
\(\dfrac{30x^6y^3(x-3)^2(x+5)^2}{6xy^3(x+5)}\)
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\(5x^5(x-3)^2(x+5)\)
\(\dfrac{x^2 + 10x + 24}{x^2 + x - 30}\)
- Answer
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\(\dfrac{x + 4}{x - 5}\)
\(\dfrac{8x^2 + 2x - 3}{4x^2 + 12x - 7}\)
- Answer
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\(\dfrac{4x + 3}{2x + 7}\)
Replace \(N\) with the proper quantity.
\(\dfrac{x+2}{x-1} = \dfrac{N}{x^2 - 4x + 3}\)
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\((x−3)(x+2)\)
Assume that \(a^2 + a - 6, a^2 - a - 12\), and \(a^2 - 2a - 8\) are denominators of rational expressions. Find the LCD.
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\((a+2)(a−2)(a+3)(a−4)\)
For the following problems, perform the operations.
\(\dfrac{3a + 4}{a + 6} - \dfrac{2a - 1}{a + 6}\)
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\(\dfrac{a+5}{a+6}\)
\(\dfrac{18x^3y}{5a^2} \cdot \dfrac{15a^3b}{6x^2y}\)
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\(9abx\)
\(\dfrac{y^2-y-12}{y^2 + 3y + 2} \cdot \dfrac{y^2 + 10y + 16}{y^2 - 7y + 12}\)
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\(\dfrac{(y+3)(y+8)}{(y+1)(y-3)}\)
\(\dfrac{y-2}{y^2 - 11y + 24} + \dfrac{y + 4}{y^2 + 3y - 18}\)
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\(\dfrac{2(y^2 - 22)}{(y-8)(y-3)(y+6)}\)
\(\dfrac{9}{2x + 7} + \dfrac{4}{6x - 1}\)
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\(\dfrac{62x + 19}{(2x + 7)(6x - 1)}\)
\(\dfrac{16x^5(x^2 - 1)}{9x - 9} \div \dfrac{2x^2 - 2x}{3}\)
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\(\dfrac{8x^4(x + 1)}{3(x-1)}\)
\((m + 3) \div \dfrac{2m + 6}{5m + 1}\)
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\(\dfrac{5m + 1}{2}\)
\(\dfrac{3y + 10}{8y^2 + 10y - 3} - \dfrac{5y - 1}{4y^2 + 23y - 6}\)
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\(\dfrac{-7y^2 + 15y + 63}{(4y-1)(2y + 3)(y + 6)}\)
Solve \(\dfrac{1}{x+3} + \dfrac{3}{x-3} = \dfrac{x}{x^2 - 9}\)
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\(x = -2\)
Solve \(\dfrac{12}{m-4} + 5 = \dfrac{3m}{m-4}\).
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No solution; \(m=4\) is excluded.
When the same number is added to both the numerator and denominator of the fraction \(\dfrac{5}{3}\), the result is \(\dfrac{6}{5}\). What is the number that is added?
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\(7\)
Person A, working alone, can complete a job in 20 hours. Person B, working alone, can complete the same job in 30 hours. How long will it take both people, working together, to complete the job?
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12 hours
The width of a rectangle is 1 foot longer than one-half the length. Find the dimensions (lengh and width) of the rectangle if the perimeter is 44 feet.
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8 ft by 14 ft
Simplify the complex fraction \(\dfrac{4 - \frac{3}{x}}{4 + \frac{3}{x}}\)
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\(\dfrac{4x - 3}{4x + 3}\)
Simplify the complex fraction \(\dfrac{1-\frac{5}{x}-\frac{6}{x^{2}}}{1+\frac{6}{x}+\frac{5}{x^{2}}}\)
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\(\dfrac{x-6}{x + 5}\)
Perform the division: \(\dfrac{x^3 + 10x^2 + 21x - 18}{x + 6}\)
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\(x^2 + 4x - 3\)
Perform the division: \(\dfrac{2x^3 + 5x - 1}{x - 2}\)
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\(2x^2 + 4x + 13 + \dfrac{25}{x - 2}\)


6.5: Harmonic Waves
We are often interested in waves undergoing harmonic oscillation , i.e. varying sinusoidally with a constant frequency \(\omega\) everywhere in space. Such waves can be described by wavefunctions of the form \[f(x,y,z,t) = \psi(x,y,z) \, e^{-i\omega t}.\] By writing the wavefunction in this form, we are performing a separation of variables between \(\vec{r}\) and \(t\) . This is a common method for simplifying PDEs, and is justified by the linearity of the wave equation. If we can find harmonic solutions for each frequency \(\omega\) , we can linearly combine them to construct more general solutions that are non-harmonic.
By direct substitution into Eq. (6.4.1), we can show that \(\psi(x)\) obeys \[\left[\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} + \left(\frac{\omega}{v}\right)^2\right] \, \psi(x,y,z) = 0.\] This is related to the original time-dependent wave equation by the replacement of \(\partial/\partial t\) with \(-i\omega\) .
Waves in complex media
So far, our discussion has been limited to waves propagating in a uniform, energy-conserving medium with a fixed wave speed \(v\) . There are two important generalizations of this scenario: (i) non-uniform media, in which the wave speed varies with position, and (ii) energy non-conserving media, in which the waves lose or gain energy as they propagate. To capture these phenomena, we replace the constant \(v\) by \[v = \frac{c}{n},\] where \(n\) is called the refractive index , and the constant \(c\) is the wave speed in the limit \(n = 1\) . In the case of electromagnetic waves, \(c\) is the speed of light in a vacuum.
If the refractive index is now allowed to vary with position, the wave equation in the harmonic representation becomes \[\left[\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} + n^2(x,y,z)\, \left(\frac{\omega}{c}\right)^2\right] \, \psi(x,y,z) = 0.\]
Wave amplification and attenuation
By allowing the refractive index \(n\) to be complex , the wave equation can describe the phenomena of wave amplification (which is also called gain ) and wave attenuation (also called loss ). Amplified and attenuated waves occur in many different contexts in physics; for example, the amplification of light waves is the underlying basis for the laser.
To study these phenomena, let us go back to one-dimensional space and the simple scenario of a position-independent refractive index. For harmonic waves, the wave equation reduces to \[\left[\frac{d^2}{d x^2} + n^2\, \left(\frac{\omega}{c}\right)^2\right] \, \psi(x) = 0.\] We now let \(n\) be complex, while keeping \(\omega\) and \(c\) as positive real numbers. The solutions to the ODE have the form \[\psi(x) = A \exp\left(\pm \frac{in\omega}{c}x\right),\;\;\;\mathrm{where}\;\; A \in \mathbb{C}. \label{eq:gainloss-wave}\] Let us write the complex refractive index as \[n = n' + i n'',\quad \textrm{where}\;\, n',n'' \in \mathbb{R}.\] Then \[\psi(x) = A \exp\left[\pm in'(\omega/c)x\right]\, \exp\left[\mp n''(\omega/c)x\right].\] The first exponential factor describes the oscillation of the wavefunction, with the \(\pm\) sign determining whether the harmonic wave is moving to the right or to the left. The second exponential describes the amplification or attenuation of the wave. If \(n'' \ne 0\) , the amplitude varies exponentially with \(x\) . Thus, depending on the signs of the various parameters, the wave might grow exponentially along its direction of propagation, which corresponds to amplification, or decrease exponentially along its direction of propagation, which corresponds to damping.


6.13: Introduction to Current Trends in Organization and Job Design
What you’ll learn to do: describe current trends in organization and job design
The Industrial Revolution model of structure, which was largely modeled after military structure, has been fading in popularity and prevalence over the last twenty years. The move to flatter organizational structure with greater autonomy given to employees is highlighted by companies such as Apple and Microsoft. Ironically, the U.S. military is also moving to highly autonomous, self-organizing teams.
Contributors and Attributions
CC licensed content, Original
- Introduction to Current Trends in Organization and Job Design . Authored by : David J. Thompson, PhD, and Lumen Learning. License : CC BY: Attribution