An Purdue University course homepage
https://www.math.purdue.edu/~zhan1966/teaching/353.html
MA 353, Section 001/015, Spring 2021
2021-01-01
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<h4><b>L</b> Tuesday/Thursday Section 015: 1:30pm-2:45pm;  Section 001: 3:00-4:45pm. Zoom streaming: <a href="https://purdue.brightspace.com/"> Brightspace</a>-&gt;content-&gt;Left Panel-&gt;Zoom)<br/>
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<h4><a href="mailto:zhan1966@purdue.edu">zhan1966@purdue.edu</a></h4>
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<h4><a href="https://purdue.brightspace.com/">Brightspace</a>-&gt;content-&gt;Left Panel-&gt;Homework &amp; Office hours<a href="https://www.piazza.com/purdue/spring2021/ma353"> <br/>
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<h4><a href="https://www.piazza.com/purdue/spring2021/ma353">
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</blockquote>
<ul>
<li><b>Announcement</b>
<ul>
<li>NO CLASSES on  Mar 18 and April 13 (Reading Day).</li>
<li>Tentative in-class midterm exam dates: Feb 18 (Midterm
 I) and Mar 25 (Midterm II).</li>
</ul>
</li>
</ul>
<br/>
<ul>
<li><b>Course information</b> </li>
</ul>
<ul>
<ul>
<li>Textbook:  Linear Algebra (5th edition) by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence. </li><li>Weekly handwritten homework is due through Gradescope (linked in <a href="https://purdue.brightspace.com/">Brightspace</a>) before class on each Thursday. Grades and solutions will be posted on <a href="https://purdue.brightspace.com/">Brightspace</a>.
 Late homework will not be accepted but the lowest two
 scores of homework will be dropped in the final grading.<br/>
</li></ul></ul><ul><ul><li><a href="https://www.math.purdue.edu/~zhan1966/teaching/353/Syllabus.pdf">Syllabus</a>.</li>
<li></li>
</ul></ul>
<ul>
</ul>
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 MA 35301 Section 001/015, Spring 2021

 LINEAR ALGEBRA II

 Lectures: LAMB 108, Tuesday/Thursday Section 015: 1:30pm-2:45pm; Section 001: 3:00-4:45pm. Zoom streaming: Brightspace->content->Left Panel->Zoom)
   
 Instructor: Xiangxiong Zhang  
   
 Office: MATH 406   
   
 Email: zhan1966@purdue.edu  
   
 Virtual Office Hours: via zoom (Brightspace->content->Left Panel->Homework & Office hours) 
   
 
 * Announcement
 + NO CLASSES on Mar 18 and April 13 (Reading Day).
 + Tentative in-class midterm exam dates: Feb 18 (Midterm I) and Mar 25 (Midterm II).

 * Course information
 + Textbook: Linear Algebra (5th edition) by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence.
 + Weekly handwritten homework is due through Gradescope (linked in Brightspace) before class on each Thursday. Grades and solutions will be posted on Brightspace. Late homework will not be accepted but the lowest two scores of homework will be dropped in the final grading.
 + Syllabus.
 + Schedule, handwritten homework assignments , and due dates ( subject to change ).
 Week Dates Sections in Book Handwritten Homework Due Dates
 1 01/19 1.2 Lecture Notes HW#1 01/28 
 01/21 1.3-1.5 Lecture Notes 
 2 01/26 1.6, 2.1 Lecture Notes HW#2 02/04 
 01/28
 3 02/02 2.1-2.4 Lecture Notes HW#3 02/11 
 02/04
 4 02/09 2.5, 3.1-3.3 Lecture Notes HW#4 02/17 
 02/11 3.2-3.4 Lecture Notes 
 5 02/16 Review No HW 
 02/18 In-Class Midterm I 
 6 02/23 4.1-4.2 Lecture Notes HW#5 03/04 
 02/25 4.3-4.4 Lecture Notes 
 7 03/02 5.1 Lecture Notes HW#6 03/11 
 03/04 2.5, 5.1-5.2 Lecture Notes
 8 03/09 5.1-5.2 Lecture Notes No HW 
 03/11 6.1 Lecture Notes 
 9 03/16 6.2 Lecture Notes HW#7 03/23 
 03/18 NO CLASS (Reading Day) 
 10 03/23 Review No HW 
 03/25 In-Class Midterm II 
 11 03/30 6.2-6.3 Lecture Notes HW#8 04/08 
 04/01 6.3 Lecture Notes 
 12 04/06 6.4 Lecture Notes HW#9 04/15 
 04/08 6.5 Lecture Notes 
 13 04/13 NO CLASS (Reading Day) HW#10 04/22 
 04/15 6.5 Lecture Notes 
 14 04/20 Spectral Theoerm; HW#11 04/29 
 SVD; Jordan Form Lecture Notes 
 04/22 Applications 
 15 04/27 NO CLASS No HW; Do Practice 
  Problems on Brightspace 
 04/29 Review 
 16 05/04 Final Exam: May 4, 3:30pm-5:30pm, RAWL 1086 
  
 05/06
 


L Tuesday/Thursday Section 015: 1:30pm-2:45pm;  Section 001: 3:00-4:45pm. Zoom streaming:  Brightspace-&gt;content-&gt;Left Panel-&gt;Zoom)
 
 
 
 zhan1966@purdue.edu 
 Brightspace-&gt;content-&gt;Left Panel-&gt;Homework &amp; Office hours 
 
 
 
 Announcement
NO CLASSES on  Mar 18 and April 13 (Reading Day).
Tentative in-class midterm exam dates: Feb 18 (Midterm
 I) and Mar 25 (Midterm II).
 Course information 
Textbook:  Linear Algebra (5th edition) by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence.  Weekly handwritten homework is due through Gradescope (linked in Brightspace) before class on each Thursday. Grades and solutions will be posted on Brightspace.
 Late homework will not be accepted but the lowest two
 scores of homework will be dropped in the final grading.
      Syllabus.
MA 353, Section 001/015, Spring 2021
https://www.math.purdue.edu/~zhan1966/teaching/353.html
https://www.purdue.edu/fnr/extension/
Purdue Extensio- Forestry & Natural Resources
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Posted: February 2, 2023 in Forestry, Forests and Street Trees, Gardening, How To, Wildlife 
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Posted: January 30, 2023 in Forestry, Forests and Street Trees, How To, Plants, Urban Forestry, Wildlife, Woodlands 
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Posted: January 18, 2023 in Forestry, How To, Timber Marketing, Wildlife, Woodlands 
 	
 
 
 
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http://quanser.blogspot.com/2013/12/controls-course-gives-students-skills.html
Controls Course Gives Students Skills and Tools for Senior Design Project and Future Career
2013-12-17
Quanser
<div><div><p>
The <a href="https://engineering.purdue.edu/ME">School of Mechanical Engineering</a> at the Purdue University has a rather large enrollment, with more than 1,300 students in sophomore to senior years. The School strives to graduate engineers with knowledge and skills they will use in their career paths once they leave the university. Providing them with the tools and equipment similar to those used in industry is therefore a must.</p><p>
A great example of a course that adapted to the changing environment is the Automatic Control Systems Course. While the controller design techniques and theories that students learn are still sound, the course lab had to be updated to reflect the shift in the controllers hardware implementation. As a result, students learn controller design methods working with <a href="http://www.quanser.com/NI-Quanser">Quanser-NI platform</a>. Since the focus of the course lies on the controller design, rather than on programming or plant analysis, the School has decided to equip the lab with several NI<a href="http://www.ni.com/compactrio/"> CompactRIO</a> controllers that can be easily connected to a Quanser plant, such as a <a href="http://www.quanser.com/products/linear_servo_IP02">Linear Inverted Pendulum</a> or <a href="http://www.quanser.com/Products/seesaw">Seesaw</a>.</p><table><tbody>
<tr><td><a href="http://1.bp.blogspot.com/-MT312gozUmc/Uqt764RoLDI/AAAAAAAADEk/jQbPtSKV3Ug/s1600/Linear+IP+lab.jpg"></a></td></tr>
<tr><td>A typical lab setup as presented by Dr. Galen King, Professor of Mechanical Engineering at Purdue University during the recent NI Engineering Education webcast series.</td><td></td><td><br /></td></tr>
</tbody></table><p>
At the beginning of the course, students learn to design their controller based on the method covered in the class, using <a href="http://www.ni.com/labview/">LabVIEW</a> Control Design and Simulation Module. Once they validate their algorithm in simulation, they deploy the code to the cRIO system, using LabVIEW to program FPGA on the cRIO module. At the end of semester, students complete their project by implementing the controller on an actual physical plant - either a custom build one, or on a linear motion control system from Quanser. That allows them to observe the behavior of the plant and tune their controller. At the end of the semester the students can compare their designs in a contest. They even take Quanser Seesaw further, to make the contest more exciting: students have to come up with the controller to balance the seesaw as weights are added on one end.</p><p>
The course has been very well received by the students. By the end of the course, they are able to design real-time controllers on their own and are quite happy with the minimal programming overhead using LabVIEW environment. Moreover, they are able to apply the control concepts during their Capstone Design Project - and several students are competing to use the cRIO controllers they became familiar with in the Automatic Control Systems Course.</p><p>
That's exactly what the Quanser-NI platform is supposed to do - make controls engineering teaching more engaging, while giving students industry-related tools and build the skills they will need as professional engineers.</p><p>
To learn more about Quanser-NI platform for controls, <a href="http://www.quanser.com/NI-Quanser">click her</a>e.
</p>
</div>||||I|||| Tuesday, December 17, 2013

 Controls Course Gives Students Skills and Tools for Senior Design Project and Future Career

 The School of Mechanical Engineering at the Purdue University has a rather large enrollment, with more than 1,300 students in sophomore to senior years. The School strives to graduate engineers with knowledge and skills they will use in their career paths once they leave the university. Providing them with the tools and equipment similar to those used in industry is therefore a must.

 A great example of a course that adapted to the changing environment is the Automatic Control Systems Course. While the controller design techniques and theories that students learn are still sound, the course lab had to be updated to reflect the shift in the controllers hardware implementation. As a result, students learn controller design methods working with Quanser-NI platform. Since the focus of the course lies on the controller design, rather than on programming or plant analysis, the School has decided to equip the lab with several NI CompactRIO controllers that can be easily connected to a Quanser plant, such as a Linear Inverted Pendulum or Seesaw.

    
 A typical lab setup as presented by Dr. Galen King, Professor of Mechanical Engineering at Purdue University during the recent NI Engineering Education webcast series. 
 
 At the beginning of the course, students learn to design their controller based on the method covered in the class, using LabVIEW Control Design and Simulation Module. Once they validate their algorithm in simulation, they deploy the code to the cRIO system, using LabVIEW to program FPGA on the cRIO module. At the end of semester, students complete their project by implementing the controller on an actual physical plant - either a custom build one, or on a linear motion control system from Quanser. That allows them to observe the behavior of the plant and tune their controller. At the end of the semester the students can compare their designs in a contest. They even take Quanser Seesaw further, to make the contest more exciting: students have to come up with the controller to balance the seesaw as weights are added on one end.

 The course has been very well received by the students. By the end of the course, they are able to design real-time controllers on their own and are quite happy with the minimal programming overhead using LabVIEW environment. Moreover, they are able to apply the control concepts during their Capstone Design Project - and several students are competing to use the cRIO controllers they became familiar with in the Automatic Control Systems Course.

 That's exactly what the Quanser-NI platform is supposed to do - make controls engineering teaching more engaging, while giving students industry-related tools and build the skills they will need as professional engineers.

 To learn more about Quanser-NI platform for controls, click here.
 Posted by Quanser at 11:25 AM
 Labels: Solutions - Linear Motion Control , Solutions - Quanser-NI Workstations

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The School of Mechanical Engineering at the Purdue University has a rather large enrollment, with more than 1,300 students in sophomore to senior years. The School strives to graduate engineers with knowledge and skills they will use in their career paths once they leave the university. Providing them with the tools and equipment similar to those used in industry is therefore a must. 
A great example of a course that adapted to the changing environment is the Automatic Control Systems Course. While the controller design techniques and theories that students learn are still sound, the course lab had to be updated to reflect the shift in the controllers hardware implementation. As a result, students learn controller design methods working with Quanser-NI platform. Since the focus of the course lies on the controller design, rather than on programming or plant analysis, the School has decided to equip the lab with several NI CompactRIO controllers that can be easily connected to a Quanser plant, such as a Linear Inverted Pendulum or Seesaw.  
     
 A typical lab setup as presented by Dr. Galen King, Professor of Mechanical Engineering at Purdue University during the recent NI Engineering Education webcast series.      
  
At the beginning of the course, students learn to design their controller based on the method covered in the class, using LabVIEW Control Design and Simulation Module. Once they validate their algorithm in simulation, they deploy the code to the cRIO system, using LabVIEW to program FPGA on the cRIO module. At the end of semester, students complete their project by implementing the controller on an actual physical plant - either a custom build one, or on a linear motion control system from Quanser. That allows them to observe the behavior of the plant and tune their controller. At the end of the semester the students can compare their designs in a contest. They even take Quanser Seesaw further, to make the contest more exciting: students have to come up with the controller to balance the seesaw as weights are added on one end. 
The course has been very well received by the students. By the end of the course, they are able to design real-time controllers on their own and are quite happy with the minimal programming overhead using LabVIEW environment. Moreover, they are able to apply the control concepts during their Capstone Design Project - and several students are competing to use the cRIO controllers they became familiar with in the Automatic Control Systems Course. 
That's exactly what the Quanser-NI platform is supposed to do - make controls engineering teaching more engaging, while giving students industry-related tools and build the skills they will need as professional engineers. 
To learn more about Quanser-NI platform for controls, click here.
Controls Course Gives Students Skills and Tools for Senior Design Project and Future Career
http://quanser.blogspot.com/2013/12/controls-course-gives-students-skills.html
http://groups.csail.mit.edu/mac/users/gjs/6946/index.html
Classical Mechanics: A Computational Approach
2014-01-01
None
<div>
 
<b>MASSACHVSETTS INSTITVTE OF TECHNOLOGY</b><br /> 
Joint Subject Offering: 6.946J, 8.351J, 12.620J 
<p>
<b>Classical Mechanics:
A Computational Approach</b><br /> 
</p><p>
<a href="http://swiss.csail.mit.edu/users/wisdom/">
Jack Wisdom</a>, wisdom@mit.edu, 54-414, x3-7730 
<br />
<a href="http://groups.csail.mit.edu/mac/users/gjs/">
Gerald Jay Sussman</a>, gjs@mit.edu, 32G-514, x3-5874
<br />
</p><p>
 Kenny Chen, kclisp@mit.edu, will assist us this term.
</p>
<p>
 
 
</p>
<p>
 <b>
Content:
 </b>
</p>
<p>
We study the fundamental principles of classical mechanics, with
a modern emphasis on the qualitative structure of phase space. We
use computational ideas to formulate the principles of mechanics
precisely. Expression in a computational framework encourages clear
thinking and active exploration.
</p>
<p>
Our presentation is unusual in that computation underlies our
understanding of the mathematical ideas used to express mechanics. We
make our mathematical notations explicit and precise enough that they
can be interpreted automatically by a computer. As a consequence of
this requirement the formulas and equations stand on their own. They
have clear meaning, independent of any informal context.
</p>
<p>
We plan to consider the following topics: The Lagrangian formulation.
Action, variational principles, and equations of motion. Hamilton's
principle. Conserved quantities. Hamiltonian formulation and
canonical equations. Surfaces of section. Chaos. Canonical
transformations and generating functions. Hamilton-Jacobi theory,
Liouville's theorem and Poincaré integral invariants. Canonical
perturbation theory. Poincaré-Birkhoff and KAM theorems. Invariant
curves. Nonlinear resonances. Resonance overlap and transition to
chaos. Properties of chaotic motion.
</p>
<p>
Ideas will be illustrated and supported with physical examples. We
will make extensive use of computing to capture methods, for
simulation, and for symbolic analysis.
</p>
<hr />
<p>
This subject awards G-LEVEL Graduate Credit, however the subject
is appropriate for undergraduates who have the prerequisite experience.
Undergraduates are welcome.
</p>
<p>
Prerequisites: 8.01, 18.03, programming experience
</p>
<p>
Lectures: MWF at 1400EDT (2:00PM EDT), Online: see below
Computer Lab: Wednesday evenings, 1900-2200 EDT (7--10 PM EDT), Online
Units: 3-3-6
</p>
<p>
 Instructions for attending the online class are
 <a href="http://groups.csail.mit.edu/mac/users/gjs/6946/first-class-info.txt"> here </a>
</p>
<p>
 <b>
Teaching plan:
 </b>
</p>
<p>
Professors Jack Wisdom (EAPS) and Gerald Jay Sussman will teach
this class entirely online, with synchronous lectures on Monday,
Wednesday, and Friday at 1400--1500 EDT (2:00PM--3:00PM). We
will run our evening laboratory, each Wednesday from 1900--2200
EDT (7:00PM--10:00PM). We expect students to actively
participate in all of the meetings, so it may be difficult for
students who are in some time zones. If a significant number of
students want the hours to be modified, we will be happy to
adjust, as appropriate, (one advantage of online teaching is that
there is not a problem with allocating a classroom!) The times
can be renegotiated by the class in the first few meetings of the
term.
</p>
<p>
We also invite students individually and in groups to drop in
(online) to discuss problems with us at other times. We will try
to make ourselves very accessible in these strange circumstances.
</p>
<p>
 <b>
Grades:
 </b>
</p>
<p>
This is an advanced class. There are no quizzes. Grades are entirely
determined by the work that students do in weekly problem sets,
attendance and participation in the class and in the laboratory, and
some more extensive projects. In the evening laboratory we hang out
with the students, engage in discussions, and we try to help with the
weekly work. We encourage students to work together and help each
other learn the material, but each student must prepare an individual
report on the work done on the problem sets and projects. Each
student must report on the help that they gave to and received from
other students.
</p>
<p>
 <b>
Textbook: 
 </b>
</p>
<p>
<a href="https://mitpress.mit.edu/books/structure-and-interpretation-classical-mechanics-second-edition">
Structure and Interpretation of Classical Mechanics, second edition</a>,
MIT Press, 2014, ISBN: 978-0-262-02896-7
</p><p>
<a href="http://mitpress.mit.edu/sites/default/files/titles/content/sicm_edition_2/book.html">
Structure and Interpretation of Classical Mechanics (HTML free!), second edition</a>
</p><p>
<a href="http://groups.csail.mit.edu/mac/users/gjs/6946/errata.pdf">
Errata for the Mechanics Book, second edition </a>. 
</p><p>
 <b>
Class Organization: 
 </b>
</p>
<p>
<a href="http://groups.csail.mit.edu/mac/users/gjs/6946/red-tape.pdf">
Red Tape Memo</a>
</p>
<p>
<a href="http://groups.csail.mit.edu/mac/users/gjs/6946/assignments.html">
Assignments</a>
</p>
<p>
 <b>
Other Resources: 
 </b>
</p>
<p>
<a href="http://mitpress.mit.edu/sicp/full-text/book/book.html">
Structure and Interpretation of Computer Programs, second edition (HTML) </a>
</p>
<p>
 <a href="dont-panic">Don't Panic!</a>: A guide for the perplexed (software setup).
</p>
<p>
<a href="http://groups.csail.mit.edu/mac/users/gjs/6946/beginner.pdf">
Beginner notes</a>
</p>
<p>
<a href="http://groups.csail.mit.edu/mac/users/gjs/6946/cheat-sheet.pdf">
Edwin cheat sheet</a>
</p>
<p>
<a href="http://groups.csail.mit.edu/mac/users/gjs/6946/refman.pdf">
Scmutils manual</a>
</p>
<p>
<a href="http://groups.csail.mit.edu/mac/users/gjs/6946/graphing.pdf">
Graphing notes</a>
</p>
<p>
<b>
 Software:
</b>
</p>
<p>
If you want to install the software on your personal computers 
see <a href="http://groups.csail.mit.edu/mac/users/gjs/6946/installation.html"> here</a>. 
</p>
<p>
We also make our software available on Athena.
</p>
<p>
Because our laboratory will be online this year (UGH!) we are also developing
a special collaborative software system that we will use in the lab!
</p>
<p>
 <b>
Plug for our other book, not needed for this class: 
 </b>
</p>
<p>
<a href="http://mitpress.mit.edu/books/functional-differential-geometry">
Our MIT Press book on differential geometry!</a>
</p>
<p>
<b>
Software for Differential Geometry:
</b>
</p>
<p>
This software is now automatically part of our mechanics system, available above.
</p>
<br />
||||I||||MASSACHVSETTS INSTITVTE OF TECHNOLOGY
Joint Subject Offering: 6.946J, 8.351J, 12.620J

Classical Mechanics: A Computational Approach

Jack Wisdom, wisdom@mit.edu, 54-414, x3-7730
Gerald Jay Sussman, gjs@mit.edu, 32G-514, x3-5874

Kenny Chen, kclisp@mit.edu, will assist us this term.

Content:

We study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.

Our presentation is unusual in that computation underlies our understanding of the mathematical ideas used to express mechanics. We make our mathematical notations explicit and precise enough that they can be interpreted automatically by a computer. As a consequence of this requirement the formulas and equations stand on their own. They have clear meaning, independent of any informal context.

We plan to consider the following topics: The Lagrangian formulation. Action, variational principles, and equations of motion. Hamilton's principle. Conserved quantities. Hamiltonian formulation and canonical equations. Surfaces of section. Chaos. Canonical transformations and generating functions. Hamilton-Jacobi theory, Liouville's theorem and Poincaré integral invariants. Canonical perturbation theory. Poincaré-Birkhoff and KAM theorems. Invariant curves. Nonlinear resonances. Resonance overlap and transition to chaos. Properties of chaotic motion.

Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis.

This subject awards G-LEVEL Graduate Credit, however the subject is appropriate for undergraduates who have the prerequisite experience. Undergraduates are welcome.

Prerequisites: 8.01, 18.03, programming experience

Lectures: MWF at 1400EDT (2:00PM EDT), Online: see below Computer Lab: Wednesday evenings, 1900-2200 EDT (7--10 PM EDT), Online Units: 3-3-6

Instructions for attending the online class are here

Teaching plan:

Professors Jack Wisdom (EAPS) and Gerald Jay Sussman will teach this class entirely online, with synchronous lectures on Monday, Wednesday, and Friday at 1400--1500 EDT (2:00PM--3:00PM). We will run our evening laboratory, each Wednesday from 1900--2200 EDT (7:00PM--10:00PM). We expect students to actively participate in all of the meetings, so it may be difficult for students who are in some time zones. If a significant number of students want the hours to be modified, we will be happy to adjust, as appropriate, (one advantage of online teaching is that there is not a problem with allocating a classroom!) The times can be renegotiated by the class in the first few meetings of the term.

We also invite students individually and in groups to drop in (online) to discuss problems with us at other times. We will try to make ourselves very accessible in these strange circumstances.

Grades:

This is an advanced class. There are no quizzes. Grades are entirely determined by the work that students do in weekly problem sets, attendance and participation in the class and in the laboratory, and some more extensive projects. In the evening laboratory we hang out with the students, engage in discussions, and we try to help with the weekly work. We encourage students to work together and help each other learn the material, but each student must prepare an individual report on the work done on the problem sets and projects. Each student must report on the help that they gave to and received from other students.

Textbook:

Structure and Interpretation of Classical Mechanics, second edition, MIT Press, 2014, ISBN: 978-0-262-02896-7

Structure and Interpretation of Classical Mechanics (HTML free!), second edition

Errata for the Mechanics Book, second edition .

Class Organization:

Red Tape Memo

Assignments

Other Resources:

Structure and Interpretation of Computer Programs, second edition (HTML)

Don't Panic!: A guide for the perplexed (software setup).

Beginner notes

Edwin cheat sheet

Scmutils manual

Graphing notes

Software:

If you want to install the software on your personal computers see here.

We also make our software available on Athena.

Because our laboratory will be online this year (UGH!) we are also developing a special collaborative software system that we will use in the lab!

Plug for our other book, not needed for this class:

Our MIT Press book on differential geometry!

Software for Differential Geometry:

This software is now automatically part of our mechanics system, available above.


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MASSACHVSETTS INSTITVTE OF TECHNOLOGY  
Joint Subject Offering: 6.946J, 8.351J, 12.620J 
Classical Mechanics:
A Computational Approach  
 
Jack Wisdom, wisdom@mit.edu, 54-414, x3-7730 
Gerald Jay Sussman, gjs@mit.edu, 32G-514, x3-5874
 
 Kenny Chen, kclisp@mit.edu, will assist us this term.
 
 
 
Content:
 
We study the fundamental principles of classical mechanics, with
a modern emphasis on the qualitative structure of phase space. We
use computational ideas to formulate the principles of mechanics
precisely. Expression in a computational framework encourages clear
thinking and active exploration.
Our presentation is unusual in that computation underlies our
understanding of the mathematical ideas used to express mechanics. We
make our mathematical notations explicit and precise enough that they
can be interpreted automatically by a computer. As a consequence of
this requirement the formulas and equations stand on their own. They
have clear meaning, independent of any informal context.
We plan to consider the following topics: The Lagrangian formulation.
Action, variational principles, and equations of motion. Hamilton's
principle. Conserved quantities. Hamiltonian formulation and
canonical equations. Surfaces of section. Chaos. Canonical
transformations and generating functions. Hamilton-Jacobi theory,
Liouville's theorem and Poincaré integral invariants. Canonical
perturbation theory. Poincaré-Birkhoff and KAM theorems. Invariant
curves. Nonlinear resonances. Resonance overlap and transition to
chaos. Properties of chaotic motion.
Ideas will be illustrated and supported with physical examples. We
will make extensive use of computing to capture methods, for
simulation, and for symbolic analysis.
This subject awards G-LEVEL Graduate Credit, however the subject
is appropriate for undergraduates who have the prerequisite experience.
Undergraduates are welcome.
Prerequisites: 8.01, 18.03, programming experience
Lectures: MWF at 1400EDT (2:00PM EDT), Online: see below
Computer Lab: Wednesday evenings, 1900-2200 EDT (7--10 PM EDT), Online
Units: 3-3-6
 Instructions for attending the online class are
  here 
 
Teaching plan:
 
Professors Jack Wisdom (EAPS) and Gerald Jay Sussman will teach
this class entirely online, with synchronous lectures on Monday,
Wednesday, and Friday at 1400--1500 EDT (2:00PM--3:00PM). We
will run our evening laboratory, each Wednesday from 1900--2200
EDT (7:00PM--10:00PM). We expect students to actively
participate in all of the meetings, so it may be difficult for
students who are in some time zones. If a significant number of
students want the hours to be modified, we will be happy to
adjust, as appropriate, (one advantage of online teaching is that
there is not a problem with allocating a classroom!) The times
can be renegotiated by the class in the first few meetings of the
term.
We also invite students individually and in groups to drop in
(online) to discuss problems with us at other times. We will try
to make ourselves very accessible in these strange circumstances.
 
Grades:
 
This is an advanced class. There are no quizzes. Grades are entirely
determined by the work that students do in weekly problem sets,
attendance and participation in the class and in the laboratory, and
some more extensive projects. In the evening laboratory we hang out
with the students, engage in discussions, and we try to help with the
weekly work. We encourage students to work together and help each
other learn the material, but each student must prepare an individual
report on the work done on the problem sets and projects. Each
student must report on the help that they gave to and received from
other students.
 
Textbook: 
 
Structure and Interpretation of Classical Mechanics, second edition,
MIT Press, 2014, ISBN: 978-0-262-02896-7
 
Structure and Interpretation of Classical Mechanics (HTML free!), second edition
 
Errata for the Mechanics Book, second edition . 
 
 
Class Organization: 
 
Red Tape Memo
Assignments
 
Other Resources: 
 
Structure and Interpretation of Computer Programs, second edition (HTML) 
 Don't Panic!: A guide for the perplexed (software setup).
Beginner notes
Edwin cheat sheet
Scmutils manual
Graphing notes
 Software:
If you want to install the software on your personal computers 
see  here. 
We also make our software available on Athena.
Because our laboratory will be online this year (UGH!) we are also developing
a special collaborative software system that we will use in the lab!
 
Plug for our other book, not needed for this class: 
 
Our MIT Press book on differential geometry!
Software for Differential Geometry:
This software is now automatically part of our mechanics system, available above.
Classical Mechanics: A Computational Approach
http://groups.csail.mit.edu/mac/users/gjs/6946/index.html