7.1: Introduction to the U.S. Court System
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- Alison S. Burke, David Carter, Brian Fedorek, Tiffany Morey, Lore Rutz-Burri, & Shanell Sanchez
- Southern Oregon University via OpenOregon
What follows is an examination of the structure and role of the courts in the American criminal justice system and the requirement of jurisdiction . As you read this chapter, pay attention to the context when you see the word “court” because it is used in a variety of ways. “Court” can mean a building—it is short for “courthouse” (for example, “he went to the court”); one judge (for example, “the trial court decided in his favor”); a group of judges (for example, “the Supreme Court unanimously upheld the conviction”), or an institution/process generally (for example, “courts hopefully resolve disputes in an even-handed manner”). Courts (the institution and processes) determine both the facts of a crime (did the defendant do the crime?) and also the legal sufficiency of the criminal charge (can the government prove it?). Courts ensure that criminal defendants are provided due process of law , or the procedures used to convict the defendant are fair. Courts are possibly more important in criminal cases than in civil cases because, in civil matters, the parties have the option of settling their disputes outside of the court system, but all criminal prosecutions must be funneled through the criminal courts.
After reading this chapter, you will be able to project the trajectory of a criminal case from the filing of criminal charges in a local courthouse through all final appeals processes. This requires an understanding of the dual court system, the structure of typical state court systems and the federal court system. This chapter explores the differences between a trial court and an appellate court, and you will learn how trial judges and juries decide (determine the outcome of) a case by applying the legal standards to the facts presented during trial and how appellate judges decide if the case was rightly decided after examining the trial record for legal error. Appellate courts make known their decisions known through their written opinions, and this chapter introduces the types of opinions and rulings of appellate courts.
This chapter also examines the selection, roles, and responsibilities of the participants in the criminal courts frequently referred to as the courtroom workgroup. You will become familiar with who the players are during each of these steps of the process.


6: Footnotes
Footnotes
1 Henderson (1998).
2 Woodman (2004) xxi.
3 We are not trying to compete with general introductions to Tacitus and his works, of which there are plenty. We particularly recommend Ash (2006) and the two recent companions to Tacitus edited by Woodman (2009a) and Pagán (2012). See also, more generally, the companions to (Greek and) Roman historiography edited by Marincola (2007) and Feldherr (2009).
4 This paragraph is based on Birley (2000) and Martin and Woodman (2012).
5 Birley (2000) 231 n. 4 with reference to Oliver (1977).
6 Birley (2000) 233–34.
7 Birley (2000) 234. Tacitus himself records his involvement at Annals 11.11.1: Isdem consulibus ludi saeculares octingentesimo post Romam conditam, quarto et sexagesimo quam Augustus ediderat, spectati sunt. utriusque principis rationes praetermitto, satis narratas libris quibus res imperatoris Domitiani composui. nam is quoque edidit ludos saecularis iisque intentius adfui sacerdotio quindecimvirali praeditus ac tunc praetor; quod non iactantia refero sed quia collegio quindecimvirum antiquitus ea cura et magistratus potissimum exequebantur officia caerimoniarum. [Under the same consulate (= 47 AD), eight hundred years from the foundation of Rome, sixty-four from their presentation by Augustus, came a performance of the Secular Games. The calculations employed by the two princes I omit, as they have been sufficiently explained in the books which I have devoted to the reign of Domitian (= the closing books, now lost, of the Histories). For he too exhibited Secular Games, and, as the holder of a quindecimviral priesthood and as praetor at the time, I followed them with more than usual care: a fact which I recall not in vanity, but because from of old this responsibility has rested with the Fifteen, and because it was to magistrates in especial that the task fell of discharging the duties connected with the religious ceremonies.]
8 Woodman (2004) xi.
9 Noreña (2011) 7. His conception of imperial Rome owes much to Paul Veyne (1976) and, in particular, Egon Flaig (1992) (2010).
10 The distinction between ‘real’ and ‘symbolic’ Noreña draws here is perhaps unhelpful – since symbolic interactions were very real as well. Presumably, though, he means to distinguish between interactions that happened face-to-face or had a material dimension and those that happened via symbolic gestures or other media of communication (coins, religious worship etc.). Some forms of interaction, such as the donative to the soldiers on special occasions, had both a material and a symbolic value.
11 The Roman principate was not a hereditary monarchy: the potential for usurpation defined the political system, even though succession frequently followed dynastic principles. See further Bert Lott (2012).
12 We owe appreciation of this point to discussions with Ulrich Gotter.
13 Annals 16.4–5.
14 Roller (2001) 6.
15 Roller (2001) 11.
16 See e.g. Lintott (2001–2003) (including discussion of the republican background) and Rutledge (2001).
17 Oakley (2012a) 188.
18 Flaig (1992) 123 n. 98.
19 Wallace-Hadrill (1982) 47.
20 http://www.youtube.com/watch?v=w-Nh-zSMzqo . For an equivalent in adult entertainment check out History Channel’s Caligula: 1400 Days of Terror.
21 For rehabilitation of Caligula see Winterling (2003/2011); for ‘Nero the Hero’ Champlin (2003). See also Caligula with Mary Beard on BBC2 (available on-line).
22 Syme (1970) 1–2.
23 See Agricola 2, where Tacitus envisions all the pursuits (such as the writing of history) that were traditionally located in aristocratic otium exiled from Rome during the reign of Domitian.
24 See further Ash (2006) 20 and, for a close reading of the preface, Woodman (2012).
25 There was a sinister side to the treatise’s history of reception as it inspired many a German nationalist after it was rediscovered in the Renaissance: see Krebs (2012).
26 We cite the text and translation by C. H. Moore in the Loeb Classical Library (Cambridge, Mass., 1925).
27 Martin (1981) 104.
28 Much like Livy 43.13.2: meos annales.
29 See Gotter and Luraghi (2003).
30 Woodman (1992).
31 Ginsberg (1981) 100: ‘Tacitus has rejected traditional annalistic history, but he has not rejected its form. There is a good reason. The annalistic form was traditionally associated with the republican past, and Tacitus wanted to evoke that past, if only to deny its application to the present. … In rejecting traditional annalistic history, Tacitus rejects also an interpretation of history.’
32 Griffin (2009) 182: ‘The structure of the Annals as a whole combines an annalistic principle, which applies to the smaller organisation within each book, and a regnal principle, which groups the books according to the reigns of emperors and which ensures that the reigns of Tiberius and Claudius (and doubtless of Caligula) each close with the end of a book.’ As Griffin goes on to show, the relative dominance of the two principles throughout the narrative varies from emperor to emperor – one of the formal means by which Tacitus generates meaning.
33 Henderson (1998) 257–58.
34 Spot the odd one out (Annals 13.58): Eodem anno Ruminalem arborem in comitio, quae octingentos et triginta ante annos Remi Romulique infantiam texerat, mortuis ramalibus et arescente trunco deminutam prodigii loco habitum est, donec in novos fetus reviresceret (‘In the same year, the Ruminal tree in the Comitium, which 830 years earlier had sheltered Remus and Romulus in their infancy, through the death of its boughs and the withering of its stem reached a stage of decrepitude which was regarded as a portent – until it revived with fresh shoots’). A portent such as the withering of a sacred tree may well have been entered in the annalistic record – but also if it then consumes itself? Is Tacitus pulling our leg here, with an unexpected, yet deconstructive, gesture to a formal device of annalistic writing?
35 This return to a coincidence of beginning of the year and beginning of the book also receives instant and ironic qualification: right after the dating, Tacitus drops the acid remark that the length of his reign (vetustate imperii – a dark-humoured hyperbole that mockingly asserts the dominance of the imperial principle) had finally rendered Nero sufficiently audacious to go through with the long-plotted matricide.
36 Our discussion in this section draws above all on Martin (1981), Henderson (1998), O’Gorman (2000), and Oakley (2009b).
37 Woodman (2009b) 14.
38 Goodyear (2012) 369.
39 Syme (1958) 347.
40 Martin (1981) 214–15.
41 Martin (1981) 220.
42 O’Gorman (2000) 3.
43 Martin (1981) 221.
44 O’Gorman (2000) 11.
45 O’Gorman (2000) 11; we give the translation of J. M. May and J. Wisse, Cicero On the Ideal Orator (De Oratore), New York and Oxford 2001.
46 O’Gorman (2000) 11.
47 See O’Gorman (2000) 2: ‘The formal structures of Tacitus’ prose embody a political judgement of the principate. Tacitean style can be seen as the manifestation in narrative of a particular historical understanding, one which is integrally linked to a senatorial view of the principate.’
48 John Henderson, per litteras.
49 Henderson (1998) 260–61.
50 See Annals 1.6.1 (on the beginning of Tiberius’ reign as princeps): primum facinus novi principatus fuit Postumi Agrippae caedes (‘The opening crime of the new principate was the murder of Agrippa Postumus’).
51 Ann. 13.15–17.
52 Ann. 14.1–9.
53 Ann. 14.60–64; 16.6.
54 Ann. 15.45; 15.60–64.
55 Ann. 16.14–35.
56 Ann. 15.67.
57 Champlin (2003) 76.
58 Suetonius, Nero 49.
59 See Syme (1958) 515–16, in a chapter on ‘Tacitus and the Greeks’.
60 Champlin (2003) 68, with page 286 n. 38 where he defines civilitas, civility, as ‘the ability of the emperor to act as an ordinary citizen, or at least as an ordinary Roman nobleman.’ See also page 291 n. 85: ‘From the beginning of the reign he had allowed the people to watch him exercise in the Campus Martius; he often declaimed in public; and he had read his own poems not only at home but in the theatre “to such universal joy” that a supplication to the gods was decreed and the poems themselves were inscribed in letters of gold and dedicated to Jupiter Capitolinus: Suetonius II . 2. These were the actions of an affable emperor, the civilis princeps.’
61 Martin (1969) 139. See also Syme (1958) II 557.
62 The phrase multo cum honore Caesaris (49) is studiously ambiguous: Caesar could be Nero – or Julius Caesar.
63 Sailor (2008) 20: ‘One telling feature of Tacitus’ treatment of Thrasea and Helvidius, then, is an understated but perceptible emphasis on their strong interest in glory.’
64 See Sailor (2008) 17: ‘what gave these men their glamour was their apparent solidarity with the cause of senatorial dignity and significance: to show adherence to a set of values shared by their peers, they had held their own lives cheap.’
65 Sailor (2008) 29–30.
66 This cut-and-paste approach, while understandable, results in a distortion of Tacitus’ overall picture of the Neronian principate. In particular the geopolitical dimension of his text, the way in which he interweaves centre and periphery, Rome and the world, disappears from view. It is important to bear in mind here that Nero’s reign ended when provincial governors decided to march on Rome.
67 The law was introduced by the bachelors (!) Marcus Papius Mutilus and Quintus Poppaeus Secundus, two of the consuls of AD 9 (hence lex Papia Poppaea). This piece of legislation was an adjustment of the more famous (and, among members of the ruling élite, highly unpopular) lex Julia de maritandis ordinibus (‘Julian law on marrying categories’) that Augustus passed in 18 BC. For further details (including our sources in translation) see Cooley (2003) 353–72.
68 For Cassius Dio, we cite the translation by Earnest Cary in the Loeb Classical Library (Cambridge, Mass. and London 1914–1927).
69 Woodman (2004) 315.
70 We owe this observation to John Henderson: ‘Claudius’ recalls Nero’s predecessor the emperor Claudius (the hero of Robert Graves’ I, Claudius), whereas ‘Timarchus’ combines the two Greek words timê (‘honour’, ‘distinction’) and archê (‘power’, ‘rule’).
71 We cite the translation by H. L. Jones in the Loeb Classical Library (Cambridge, Mass. and London, 1932), slightly adjusted.
72 In his account of the arrangement put in place by Augustus, Cassius Dio reports and shreds the ideological veneer (53.12.1–3): ‘In this way he [sc. Augustus] had his supremacy ratified by the senate and by the people as well. But as he wished even so to be thought a man of the people, while he accepted all the care and oversight of the public business, on the ground that it required some attention on his part, yet he declared he would not personally govern all the provinces, and that in the case of such provinces as he should govern he would not do so indefinitely; and he did, in fact, restore to the senate the weaker provinces, on the ground that they were peaceful and free from war, while he retained the more powerful, alleging that they were insecure and precarious and either had enemies on their borders or were able on their own account to begin a serious revolt. His professed motive in this was that the senate might fearlessly enjoy the finest portion of the empire, while he himself had the hardships and the dangers; but his real purpose was that by this arrangement the senators should be unarmed and unprepared for battle, while he alone had arms and maintained soldiers.’
73 See further Brunt (1961), with discussion of our passage at 215–17.
74 Miller (1973) 69.
75 Martin and Woodman (1989) 140.
76 Miller (1973) 70 and 64.
77 Henderson (2004) 77. Another good example is Cicero’s punning on Verres, which is also the Latin term for ‘boar’ – hence ‘Mr. Porker’.
78 Translations of Sallust here and elsewhere are taken from the Loeb Classical Library edition by J. C. Rolfe (Cambridge, Mass. and London, 1921).
79 Martin (1969) 139.
80 The translation from Livy is taken from the Loeb Classical Library edition by E. T. Sage (Cambridge, Mass. and London, 1953).
81 Hölkeskamp (2004)
82 See e.g. pro Quinto Roscio 7, pro Cluentio 197, de Domo Sua 39, pro Balbo 13 with Schofield (2009) 201–4.
83 Woodman (2004) 315.
84 Kolb (2000) 36–7.
85 Rudich (1993) 77.
86 Miller (1973) 52.
87 Syme (1958) 354.
88 Rudich (1993) 77.
89 We owe this jingle to George Lord.
90 Miller (1973) 71. The last monographic treatment of the concilia is Deininger (1965).
91 Koestermann (1968) 203.
92 Syme (1958) I 343–44.
93 Gotter and Luraghi (2003) 35.
94 Griffin (2009) 168–69.
95 For instance: in a Stoic universe, in which everything unfolds according to a predetermined chain of natural causes, gods lose their independent agency and ‘chance’ has no place. (It is therefore important to note that the passage where he seems to allude to Stoic fate is very obscure: see Martin (2001) 148–49, cited by Griffin (2009) 168 n. 2, who also points out that Tacitus does not always use fatum in the technical Stoic sense of the term.)
96 Griffin (1984) 44 with page 247 n. 44.
97 See Cassius Dio 61.21.2 and Suetonius, Nero 12.3: Instituit et quinquennale certamen primus omnium Romae more Graeco triplex, musicum gymnicum equestre, quod appellavit Neronia; dedicatisque thermis atque gymnasio senatui quoque et equiti oleum praebuit (‘He was likewise the first to establish at Rome a quinquennial contest in three parts, after the Greek fashion, that is in music, athletics, and riding, which he called the Neronia; at the same time he dedicated his baths and gymnasium, supplying every member of the senatorial and equestrian orders with oil’).
98 Griffin (1984) 247 n. 44.
99 Champion (2003) 80.
100 Varner (2005) 67. On imperial statuary see further Vout (2007) and Gladhill (2012).
101 Laelia is Nr. 2161 in Jörg Rüpke’s compendium of all religious officials from ancient Rome of whom we have any record. See Rüpke (2008).
102 See Wildfang (2006), Ch. 3: ‘Vestal initiation – the rite of captio’.
103 Koestermann (1968) 62.
104 Bartera (2011) 161. Whether this standardization ‘reflects the political irrelevance of the consuls, who become, so to speak, “sclerotic” dating devices’ (ibid.), is another matter.
105 See Diogenes Laertius, Life of Periander: ‘However, after some time, in a fit of anger, he killed his wife by throwing a footstool at her, or by a kick, when she was pregnant, having been egged on by the slanderous tales of concubines, whom he afterwards burnt alive.’ We cite the translation by R. D. Hicks in the Loeb Classical Library (Cambridge, Mass. and London, 1925) – with thanks to John Henderson for the reference.
106 Suetonius, Augustus 58.
107 Oakley (2009a) 188, with reference to 14.64.3. As he points out, the examples are innumerable – and need to be appreciated as such: ‘The instances of servile behaviour that Tacitus chronicles are legion, and all readers will have their favourites; any selection that is not copious is false to the tone of his writing.’
108 See Annals 2.69.2 and elsewhere.
109 Gradel (2002) 59.
110 See Smallwood (1967) 24; Scheid (1998) 76.
111 Hickson Hahn (2007) 238. She goes on to note the problem in terminology that ensues: ‘The term “supplication” (supplicatio) illustrates this problem [i.e. how to determine whether a visual representation of prayer constituted a petition, oath, or thanksgiving] well. The Romans used the same word to identify public days of prayer and offering for propitiation, expiation, and thanksgiving.’
112 Gurval (1995) 69.
113 Humphrey (1986) 565–66.
114 As a further point of comparison one could cite Cassius Dio’s account of the honours Augustus awarded to his nephew and son-in-law Marcellus after his death in 23 BC. It is indicative of an early stage of imperial honours, where the crossing of the divide between human and divine was still a taboo: ‘Augustus gave him a public burial after the customary eulogies, placing him in the tomb he was building, and as a memorial to him finished the theatre whose foundations had already been laid by the former Caesar and which was now called the theatre of Marcellus. And he ordered also that a golden image of the deceased, a golden crown, and a curule chair should be carried into the theatre at the Ludi Romani and should be placed in the midst of the officials having charge of the games’ (53.30).
115 French (1986) 69.
116 Furneaux (1907) 347.
117 Oakley (2009b) 200, with further examples in n. 23.
118 Oakley (2009b) 196.
119 See Tacitus, Histories 4.42. Also: Pliny, Letters 1.5.3. For the practice of delation – a new development under the principate – see Introduction Section 2 and 6. Further literature includes Lintott (2001–2003) (including discussion of the republican background) and Rutledge (2001).
120 On fama see now the magisterial treatment by Hardie (2012), with a discussion of rumour in Tacitus’ historiographical works at 288–313. Flaig (2010a) offers an analysis of rumour in Roman politics from a sociological perspective, with specific reference to the reign of Nero.
121 For the varying status of the cities in the Roman Empire see Edmundson (2006) 256–58.
122 Champlin (2003) 59–60. See Suetonius, Nero 20.3 and Annals 14.15.
123 See Maltby (1991) 78.
124 Miller (1975) 83.
125 Syme (1958) I 356.
126 For the (uncertain) text, translation, and discussion see Bartsch (1994) 103–4.
127 See Swain et al. (2007).
128 So Henderson; see further Henderson (2004) 77.
129 On the ‘informer’ see Introduction Section 2 and 6.
130 Miller (1975) 84.
131 Miller (1975) 84.
132 Miller (1975) 85.
133 Caligula, too, was reported to have harboured plans to move to Alexandria after perpetrating mass slaughter among the Roman élite – a plot that Suetonius presents as the final straw that led to his assassination. See Caligula 49.2: …periit, ingentia facinora ausus et aliquanto maiora moliens, siquidem proposuerat Antium, deinde Alexandream commigrare interempto prius utriusque ordinis electissimo quoque (‘… he perished, having dared great crimes and meditating still greater ones. For he had made up his mind to move to Antium, and later to Alexandria, after first slaying the noblest members of the two orders’).
134 We cite the text and translation of S. Morton Braund in the Loeb Classical Library (Cambridge, Mass. and London, 2004).
135 See in general Garnsey (1988).
136 Woodman (1998).
137 Woodman (1998) 172.
138 See more generally Woodman (2004) xxii: ‘given a choice of synonyms, Tacitus often varies the linguistic norm by choosing the less common: luxus (“luxuriousness”) for luxuria (“luxury”), maestitia (“sorrowfulness”) for maeror (“sorrow”), seruitium (“servitude”) for seruitus (“slavery”).’
139 Woodman (1998) 171–72.
140 Woodman (1998) 172.
141 Woodman (1998) 175.
142 For Latin terms for ‘prostitute’ see Adams (1983).
143 Woodman (1998) 175–76.
144 Cf. Annals 11.27 where Tacitus dismissively speaks of imperial Rome as a society in which there are no secrets and no topic is off-limits (in civitate omnium gnara et nihil reticente). His historiography is not least an attempt to establish a dignified voice within this sea of incessant, shameless chatter.
145 We cite the translation of Guy Lee, Horace: Odes & Carmen Saeculare, with an English version in the original metres, introduction and notes, Leeds 1998.
146 Woodman (1998) 181.
147 Woodman (1998) 184 further draws attention that Cleopatra’s last Roman lover, Mark Antony – a distant ancestor of Nero no less! – was accused by Cicero of a homosexual marriage ‘in very similar terms to those used by Tacitus about Nero’: see Philippic 2.44.
148 The most recent study of the Roman wedding is Hersch (2010).
149 Santoro L’Hoir (2006) 248.
150 A fictional comparandum occurs in the first chapter of J. K. Rowling, Harry Potter and the Half-Blood Prince: ‘The Other Minister’, where the British (Muggle) Prime Minister is held responsible by his political opponents for a series of catastrophes (some nasty murders, the collapse of a bridge, a hurriance, the dismal weather): they gloatingly explain ‘why each and every one of them was the government’s fault’.
151 See the treatments by Paul (1982), who traces the literary topos and its thematic range back to Homer’s Iliad and explores its subsequent career in ‘tragic’ historiography, and Ziolkowski (1993), who looks into the specifically Roman spin on it.
152 We cite the text and translation by H. Caplan in the Loeb Classical Library (Cambridge, Mass., 1954).
153 We cite the text and translation by D. A. Russell in the Loeb Classical Library (Cambridge, Mass., 2001).
154 Fans of J. K. Rowling’s Harry-Potter saga may wish to compare Tacitus’ passage with the ‘Fiendfyre’ that rages through the Room of Requirement in Harry Potter and the Deathly Hallows, Chapter 31: ‘The Battle of Hogwarts’: ‘It was not normal fire..: as they turned a corner the flames chased them as though they were alive, sentient, intent upon killing them.  References to Troy engulfed in flames occur at Aeneid 2.311, 327, 329, 337, 353, 374, 431, 505, 566, 600, 632, 664, 705, 758, 764).
157 Austin (1964) 135. See now also the discussion by Rossi (2004), Chapter 1: ‘The Fall of Troy: Between Tradition and Genre’, esp. 24–30: ‘Flames’.
158 See Suetonius, Caesar 6, citing from Caesar’s funeral speech for his aunt Julia, delivered in 68 BC (i.e. two year after Virgil’s birth): ‘The family of my aunt Julia is descended by her mother from the kings, and on her father’s side is akin to the immortal Gods; for the Marcii Reges (her mother’s family name) go back to Ancus Marcius, and the Julii, the family of which ours is a branch, to Venus.’
159 The following is based on O’Gorman (2000) 162–75 (‘The Game of Troy’).
160 Virgil, Aeneid 12.791-842.
161 See O’Gorman (2000) 168–71 for possible affinities between Scipio and Nero (via Livy).
162 Miller (1975) 90.
163 Miller (1975) 88.
164 See further Kraus (1994). Cicero, at de Lege Agraria 2.96, also mentions that Rome’s roads ‘are none of the best’ and its side-streets ‘of the narrowest’.
165 On famine and food supply in ancient Rome see further Garnsey (1988).
166 See Corpus Inscriptionum Latinarum VI.1, 826.
167 Miller (1973) 91.
168 Koestermann (1968) 242.
169 Furneaux (1907) 367.
170 Koestermann (1968) 242.
171 Furneaux (1907) 367, with reference to Annals 16.4.2.
172 Furneaux (1907) 368.
173 Miller (1973) 92 regards vetustissima religione as ‘a loosely attached abl. of attendant circumstances or quality.’ Cf. fessa aetate (38.4).
174 Koestermann (1968) 243.
175 Miller (1973) 93.
176 Klauck (2003).
177 Text and translation by D. R. Shackleton Bailey in the Loeb Classical Library edition (Cambridge, Mass. and London, 1993).
178 See Plutarch, Julius Caesar 58.
179 Koestermann (1968) 248.
180 Miller (1973) 95.
181 Eck (2009) 238–39.
182 Koestermann (1968) 251.
183 Miller (1973) 95.
184 See Linderski (1996) 1382.
185 Text and translation are taken from D. R. Shackleton Bailey’s Loeb edition (Cambridge, Mass. and London, 2000). With reference to the last sentence he comments in a footnote: ‘A rare touch of humour’.
186 Rives (2007) 198–99.
187 Miller (1973) xxviii.
188 Miller (1973) xxviii.
189 For a discussion of the paleographical evidence see e.g. http://www.textexcavation.com/documents/zaratacituschrestianos.pdf
190 Lichtenberg (1996) 2170.
191 Miller (1973) 96. Her reference is to the Acts of the Apostles, the fifth book of the New Testament. In the Vulgate version of the Bible, the chapter (referring to events in AD 40) reads as follows: et annum totum conversati sunt in ecclesia et docuerunt turbam multam ita ut cognominarentur primum Antiochiae discipuli Christiani (‘And they conversed there in the church a whole year: and they taught a great multitude, so that at Antioch the disciples were first named Christians’). Text and translation from http://www.latinvulgate.com/ .
192 Syme (1958) II 469.
193 Brunt (1966) 463.
194 Koestermann (1968) 256.
195 Miller (1973) 97.
196 For representations of the Actaeon story at the amphitheatre of Capua, see Bomgardner (2000) 100.
197 Lichtenberger (1996) 2171.
198 Miller (1973) 97.
199 Cicero, ad Familiares 7.1.
200 Miller (1973) 87.
201 Koestermann (1968) 262.
202 Miller (1973) 99.


2.3.4: System Regulation
Most systems tend toward a state of equilibrium where system inputs are balanced by system outputs. Though natural systems change over long periods of time, on the scale of a human lifetime they appear to be static. In reality, the state of natural systems oscillates around a mean condition a state known as dynamic equilibrium . For instance, the abundance and type of animal species in an ecosystem may fluctuate over a time, but the overall diversity remains constant. The Earth's atmospheric temperature has remained fairly constant through long periods of Earth history, even though at shorter time intervals, geologically speaking, the temperature has risen or fallen. If one or more controlling variables (climate, vegetation, soil, man) imposes a long-term stress to the system it will seek to establish a new state. A steady-state equilibrium is reached when the rates of system inputs and outputs are equal, and the amount of material stored in the system is constant over time.
The state of the system is a result of feedback mechanisms between system components.


1.1: Notes About These Notes
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This book originated from my class notes for Math 286 at the University of Illinois at Urbana-Champaign (UIUC) in Fall 2008 and Spring 2009. It is a first course on differential equations for engineers. Using this book, I also taught Math 285 at UIUC, Math 20D at University of California, San Diego (UCSD), and Math 4233 at Oklahoma State University (OSU). Normally these courses are taught with Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling [ EP ], or Boyce and DiPrima’s Elementary Differential Equations and Boundary Value Problems [ BD ], and this book aims to be more or less a drop-in replacement. Other books I used as sources of information and inspiration are E.L. Ince’s classic (and inexpensive) Ordinary Differential Equations [ I ], Stanley Farlow’s Differential Equations and Their Applications [ F ], now available from Dover, Berg and McGregor’s Elementary Partial Differential Equations [ BM ], and William Trench’s free book Elementary Differential Equations with Boundary Value Problems [ T ]. See the Further Reading chapter at the end of the book.
Organization
The organization of this book to some degree requires chapters be done in order. Later chapters can be dropped. The dependence of the material covered is roughly:
There are a few references in chapters 4 and 5 to chapter 3 (some linear algebra), but these references are not essential and can be skimmed over, so chapter 3 can safely be dropped, while still covering chapters 4 and 5 . Chapter 6 does not depend on chapter 4 except that the PDE section 6.5 makes a few references to chapter 4 , although it could, in theory, be covered separately. The more in-depth appendix A on linear algebra can replace the short review Section 3.2 for a course that combines linear algebra and ODE.
Typical Types of Courses
Several typical types of courses can be run with the book. There are the two original courses at UIUC, both cover ODE as well some PDE. Either, there is the 4 hours-a-week for a semester (Math 286 at UIUC):
Introduction ( 0.2 ), chapter 1 ( 1.1 - 1.7 ), chapter 2 , chapter 3 , chapter 4 ( 4.1 - 4.9 ), chapter 5 (or 6 or 7 or 8 ).
Or, the second course at UIUC is at 3 hours-a-week (Math 285 at UIUC):
Introduction ( 0.2 ), chapter 1 ( 1.1 - 1.7 ), chapter 2 , chapter 4 ( 4.1 - 4.9 ), (and maybe chapter 5 , 6 or 7 ).
A semester-long course at 3 hours a week that doesn’t cover either systems or PDE will cover, beyond the introduction, chapter 1 , chapter 2 , chapter 6 , and chapter 7 , (with sections skipped as above). On the other hand, a typical course that covers systems will probably need to skip Laplace and power series and cover chapter 1 , chapter 2 , chapter 3 , and chapter 8 .
If sections need to be skipped in the beginning, a good core of the sections on single ODE is: 0.2 , 1.1 - 1.4 , 1.6 , 2.1 , 2.2 , 2.4 - 2.6 .
The complete book can be covered at a reasonably fast pace at approximately 76 lectures (without appendix A ) or 86 lectures (with appendix A replacing Section 3.2 ). This is not accounting for exams, review, or time spent in a computer lab. A two-quarter or a two-semester course can be easily run with the material. For example (with some sections perhaps strategically skipped):
Semester 1:
Introduction
,
chapter 1
,
chapter 2
,
chapter 6
,
chapter 7
.
Semester 2:
Chapter 3
,
chapter 8
,
chapter 4
,
chapter 5
.
A combined course on ODE with linear algebra can run as:
Introduction , chapter 1 ( 1.1 - 1.7 ), chapter 2 , appendix A , chapter 3 (w/o Section 3.2 ), (possibly chapter 8 ).
The chapter on the Laplace transform ( chapter 6 ), the chapter on Sturm–Liouville ( chapter 5 ), the chapter on power series ( chapter 7 ), and the chapter on nonlinear systems ( chapter 8 ), are more or less interchangeable and can be treated as "topics". If chapter 8 is covered, it may be best to place it right after chapter 3 , and chapter 5 is best covered right after chapter 4 . If time is short, the first two sections of chapter 7 make a reasonable self-contained unit.
Computer Resources
The book’s website https://www.jirka.org/diffyqs/ contains the following resources:
- Interactive SAGE demos.
- Online WeBWorK homeworks (using either your own WeBWorK installation or Edfinity) for most sections, customized for this book.
- The PDFs of the figures used in this book.
I taught the UIUC courses using IODE ( https://faculty.math.illinois.edu/iode/ ). IODE is a free software package that works with Matlab (proprietary) or Octave (free software). The graphs in the book were made with the Genius software (see https://www.jirka.org/genius.html ). I use Genius in class to show these (and other) graphs.
The LaTeX source of the book is also available for possible modification and customization at github ( https://github.com/jirilebl/diffyqs ).
Acknowledgments
Firstly, I would like to acknowledge Rick Laugesen. I used his handwritten class notes the first time I taught Math 286. My organization of this book through chapter 5, and the choice of material covered, is heavily influenced by his notes. Many examples and computations are taken from his notes. I am also heavily indebted to Rick for all the advice he has given me, not just on teaching Math 286. For spotting errors and other suggestions, I would also like to acknowledge (in no particular order): John P. D’Angelo, Sean Raleigh, Jessica Robinson, Michael Angelini, Leonardo Gomes, Jeff Winegar, Ian Simon, Thomas Wicklund, Eliot Brenner, Sean Robinson, Jannett Susberry, Dana Al-Quadi, Cesar Alvarez, Cem Bagdatlioglu, Nathan Wong, Alison Shive, Shawn White, Wing Yip Ho, Joanne Shin, Gladys Cruz, Jonathan Gomez, Janelle Louie, Navid Froutan, Grace Victorine, Paul Pearson, Jared Teague, Ziad Adwan, Martin Weilandt, Sönmez Şahutoğlu, Pete Peterson, Thomas Gresham, Prentiss Hyde, Jai Welch, Simon Tse, Andrew Browning, James Choi, Dusty Grundmeier, John Marriott, Jim Kruidenier, Barry Conrad, Wesley Snider, Colton Koop, Sarah Morse, Erik Boczko, Asif Shakeel, Chris Peterson, Nicholas Hu, Paul Seeburger, Jonathan McCormick, David Leep, William Meisel, Shishir Agrawal, Tom Wan, Andres Valloud, and probably others I have forgotten. Finally, I would like to acknowledge NSF grants DMS-0900885 and DMS-1362337.


5.3: Websites
Eric Coleman’s Care Transitions Intervention Model
Care Transitions Program
The Care Transitions Intervention is a 4-week program where patients with complex care needs and family caregivers receive specific tools and work with transitions coach, to learn self-management skills that will ensure their needs are met during the transition from hospital to home. This is a low-cost, low-intensity evidence-based intervention comprised of a home visit and three phone calls.
Advance Care Planning: An Introduction for Public Health and Aging Services Professionals
Center for Disease Control, 2011.
This free online course is intended to increase understanding among public health and aging services professionals about key issues related to advance care planning for end of life, including communicating and documenting one’s wishes and preferences.


8.17E: Zygomycota - The Conjugated Fungi
- Describe the ecology and reproduction of Zygomycetes
Zygomycota: The Conjugated Fungi
The zygomycetes are a relatively small group in the fungi kingdom and belong to the Phylum Zygomycota. They include the familiar bread mold, Rhizopus stolonifer, which rapidly propagates on the surfaces of breads, fruits, and vegetables. They are mostly terrestrial in habitat, living in soil or on plants and animals. Most species are saprobes meaning they live off decaying organic material. Some are parasites of plants, insects, and small animals, while others form symbiotic relationships with plants. Zygomycetes play a considerable commercial role. The metabolic products of other species of Rhizopus are intermediates in the synthesis of semi-synthetic steroid hormones.
Zygomycetes have a thallus of coenocytic hyphae in which the nuclei are haploid when the organism is in the vegetative stage. The fungi usually reproduce asexually by producing sporangiospores. The black tips of bread mold, Rhizopus stolonifer , are the swollen sporangia packed with black spores. When spores land on a suitable substrate, they germinate and produce a new mycelium.
Sexual reproduction starts when conditions become unfavorable. Two opposing mating strains (type + and type –) must be in close proximity for gametangia (singular: gametangium) from the hyphae to be produced and fuse, leading to karyogamy. The developing diploid zygospores have thick coats that protect them from desiccation and other hazards. They may remain dormant until environmental conditions become favorable. When the zygospore germinates, it undergoes meiosis and produces haploid spores, which will, in turn, grow into a new organism. This form of sexual reproduction in fungi is called conjugation (although it differs markedly from conjugation in bacteria and protists), giving rise to the name “conjugated fungi”.
Key Points
- Most zygomycota are saprobes, while a few species are parasites.
- Zygomycota usually reproduce asexually by producing sporangiospores.
- Zygomycota reproduce sexually when environmental conditions become unfavorable.
- To reproduce sexually, two opposing mating strains must fuse or conjugate, thereby, sharing genetic content and creating zygospores.
- The resulting diploid zygospores remain dormant and protected by thick coats until environmental conditions have improved.
- When conditions become favorable, zygospores undergo meiosis to produce haploid spores, which will eventually grow into a new organism.
Key Terms
- zygomycete : an organism of the phylum Zygomycota
- karyogamy : the fusion of two nuclei within a cell
- zygospore : a spore formed by the union of several zoospores
- conjugation : the temporary fusion of organisms, especially as part of sexual reproduction


1.2.2: Basic American Legal Principles
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The American legal system has its roots in the British legal system. It was developed with the purpose of establishing standards for acceptable conduct, proscribing punishment for violations as a deterrent, establishing systems for enforcement, and peacefully resolving disputes. The ultimate goal of the American legal system is promotion of the common good.
Establishing Standards
The American legal system was developed with the goal of establishing a set of standards that outline what is to be considered minimally acceptable behavior. Broadly speaking, federal laws are those that all United States citizens are expected to follow. State and local laws may often be similar to federal laws, but they may also differ quite a bit, and only govern the state’s citizens.
Promoting Consistency
The American legal system follows the British Common Law system, which is designed to leverage past judicial reasoning, while also promoting fairness through consistency. Judges in the Common Law system help shape the law through their rulings and interpretations. This body of past decisions is known as case law . Judges use case law to inform their own rulings. Indeed, judges rely on precedent , i.e., previous court rulings on similar cases, for ruling on their own cases.
All U.S. states, except Louisiana, have enacted “reception statutes,” stating that the judge-made common law of England is the law of the state to the extent that it does not conflict with the state’s current laws.
However, the body of American law is now so robust that American cases rarely cite English materials, except for a British classic or a famous old case. Additionally, foreign law is not cited as binding precedent. Therefore, the current American practice of the common law tradition refers more to the process of judges looking to the precedent set jurisdictionally, and substantially similar to, American case law.
Maintaining Order
Congruent with the goal of establishing standards and promoting consistency, laws are also used to promote, provide, and maintain order.
Resolving Disputes
Conflicts are to be expected given people’s varying needs, desires, objectives, values systems, and perspectives. The American legal system provides a formal means for resolving conflicts through the courts. In addition to the federal court and individual state systems, there are also several informal means for resolving disputes that are collectively called alternative dispute resolution (ADR). Examples of these are mediation and arbitration.
Protecting Liberties and Rights
The United States Constitution and state laws provide people with many liberties and rights. American laws operate with the purpose and function of protecting these liberties and rights from violations by persons, companies, governments, or other entities.
Based on the British legal system, the American legal system is divided into a federal system and a state and local system. The overall goal of both systems is to provide order and a means of dispute settlement, as well as to protect citizens’ rights.
Clearly, the purposes of the American legal system are broad and well-considered.
Contributors and Attributions
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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>. Download for free at https://openstax.org/details/books/b...w-i-essentials .


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19.8: Thinking about the material
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Reflect and research
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Describe how superconductivity arises in certain materials (hint: research “Cooper pairs”).
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What are some example of superconducting materials, and at what temperature do they become superconducting?
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Is there a limit to how much current a conductor can carry?
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Does an AC current have a drift velocity? Why or why not?
To try at home
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Use Ohm’s law and the electrical information on an appliance to determine the current produced drawn by your appliance (e.g. a hair dryer).
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What is the current produced by your phone’s battery? What is the total power stored in your phone’s battery? Check the technical information of your phone.
To try in the lab
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Propose an experiment to create an AC circuit and measure its current.
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Propose an experiment to measure the temperature coefficient (
\(\alpha\)
) and resistivity of a wire.


12.6: Elasticity and Plasticity
- Explain the limit where a deformation of material is elastic
- Describe the range where materials show plastic behavior
- Analyze elasticity and plasticity on a stress-strain diagram
We referred to the proportionality constant between stress and strain as the elastic modulus . But why do we call it that? What does it mean for an object to be elastic and how do we describe its behavior?
Elasticity is the tendency of solid objects and materials to return to their original shape after the external forces (load) causing a deformation are removed. An object is elastic when it comes back to its original size and shape when the load is no longer present. Physical reasons for elastic behavior vary among materials and depend on the microscopic structure of the material. For example, the elasticity of polymers and rubbers is caused by stretching polymer chains under an applied force. In contrast, the elasticity of metals is caused by resizing and reshaping the crystalline cells of the lattices (which are the material structures of metals) under the action of externally applied forces.
The two parameters that determine the elasticity of a material are its elastic modulus and its elastic limit . A high elastic modulus is typical for materials that are hard to deform; in other words, materials that require a high load to achieve a significant strain. An example is a steel band. A low elastic modulus is typical for materials that are easily deformed under a load; for example, a rubber band. If the stress under a load becomes too high, then when the load is removed, the material no longer comes back to its original shape and size, but relaxes to a different shape and size: The material becomes permanently deformed. The elastic limit is the stress value beyond which the material no longer behaves elastically but becomes permanently deformed.
Our perception of an elastic material depends on both its elastic limit and its elastic modulus. For example, all rubbers are characterized by a low elastic modulus and a high elastic limit; hence, it is easy to stretch them and the stretch is noticeably large. Among materials with identical elastic limits, the most elastic is the one with the lowest elastic modulus.
When the load increases from zero, the resulting stress is in direct proportion to strain in the way given by Equation 12.4.4 , but only when stress does not exceed some limiting value. For stress values within this linear limit, we can describe elastic behavior in analogy with Hooke’s law for a spring. According to Hooke’s law, the stretch value of a spring under an applied force is directly proportional to the magnitude of the force. Conversely, the response force from the spring to an applied stretch is directly proportional to the stretch. In the same way, the deformation of a material under a load is directly proportional to the load, and, conversely, the resulting stress is directly proportional to strain. The linearity limit (or the proportionality limit ) is the largest stress value beyond which stress is no longer proportional to strain. Beyond the linearity limit, the relation between stress and strain is no longer linear. When stress becomes larger than the linearity limit but still within the elasticity limit, behavior is still elastic, but the relation between stress and strain becomes nonlinear.
For stresses beyond the elastic limit, a material exhibits plastic behavior . This means the material deforms irreversibly and does not return to its original shape and size, even when the load is removed. When stress is gradually increased beyond the elastic limit, the material undergoes plastic deformation. Rubber-like materials show an increase in stress with the increasing strain, which means they become more difficult to stretch and, eventually, they reach a fracture point where they break. Ductile materials such as metals show a gradual decrease in stress with the increasing strain, which means they become easier to deform as stress-strain values approach the breaking point. Microscopic mechanisms responsible for plasticity of materials are different for different materials.
We can graph the relationship between stress and strain on a stress-strain diagram . Each material has its own characteristic strain-stress curve. A typical stress-strain diagram for a ductile metal under a load is shown in Figure \(\PageIndex{1}\). In this figure, strain is a fractional elongation (not drawn to scale). When the load is gradually increased, the linear behavior (red line) that starts at the no-load point (the origin) ends at the linearity limit at point H. For further load increases beyond point H, the stress-strain relation is nonlinear but still elastic. In the figure, this nonlinear region is seen between points H and E. Ever larger loads take the stress to the elasticity limit E, where elastic behavior ends and plastic deformation begins. Beyond the elasticity limit, when the load is removed, for example at P, the material relaxes to a new shape and size along the green line. This is to say that the material becomes permanently deformed and does not come back to its initial shape and size when stress becomes zero.
The material undergoes plastic deformation for loads large enough to cause stress to go beyond the elasticity limit at E. The material continues to be plastically deformed until the stress reaches the fracture point (breaking point). Beyond the fracture point, we no longer have one sample of material, so the diagram ends at the fracture point. For the completeness of this qualitative description, it should be said that the linear, elastic, and plasticity limits denote a range of values rather than one sharp point.
The value of stress at the fracture point is called breaking stress (or ultimate stress ). Materials with similar elastic properties, such as two metals, may have very different breaking stresses. For example, ultimate stress for aluminum is 2.2 x 10 8 Pa and for steel it may be as high as 20.0 x 10 8 Pa, depending on the kind of steel. We can make a quick estimate, based on Equation 12.4.5 , that for rods with a 1-in 2 cross-sectional area, the breaking load for an aluminum rod is 3.2 x 10 4 lb, and the breaking load for a steel rod is about nine times larger.


5.4: Goal Planning
Goal planning can look different depending on the client population you serve. You will submit a treatment plan or a service plan depending on your role at the agency. For tips on writing mental health treatment plans go to: https://www.icanotes.com/2018/08/24/guide-to-creating-mental-health-treatment-plans/
For information on Individual Support Plans go to: https://www.dhs.pa.gov/Services/Disabilities-Aging/Documents/Individual%20Support%20Plan/Individual%20Support%20Plan%20(s_001649).pdf
In Module 5 of the Basic Case Management/Resource Coordination Training offered by Education and Consultative Services of UPMC Western Psychiatric Hospital in 2020, you will find some helpful information on Service Planning: https://www.oerp.pitt.edu/basic-case-management-training/ For an example of a generic Goal Plan, see the Forms section.


5.17: Ratios- Condensing Information into Smaller Pieces
By the end of this section, you will be able to:
- Explain the importance of financial statement analysis in making informed decisions about business opportunities.
- Outline the limitations of financial statement analysis in making investment decisions.
When considering the outcomes from analysis, it is important for a company to understand that the data generated needs to be compared to similar data within the industry at large as well as that of close competitors. The company should also consider its past experience and how it corresponds to current and future performance expectations.
Importance of Ratios and Analysis
Financial ratios help internal and external stakeholders make informed decisions about actions like investing, becoming a supplier, making a loan, or altering internal operations, among other things. The information resulting from ratio analysis can be used to examine trends in performance, establish benchmarks for success, set budget expectations, and compare industry competitors. There are four main types of ratios: liquidity, solvency, efficiency, and profitability. While outcomes for some ratios may seem more ideal, the industry in which the business operates can change the influence of these outcomes on stakeholder decisions.
There are several benefits to analyzing financial statements. The information can show trends over time, which can help in making future business decisions. Converting information to percentages or ratios eliminates some of the disparities between competitors’ sizes and operating abilities, making it easier for stakeholders to make informed decisions. It can assist with understanding the makeup of current operations within the business and which shifts need to occur internally to increase productivity.
Limitation of Financial Statement Analysis
Though useful, it’s important to note that there are limitations to financial statement analysis as well. Stakeholders need to remember that past performance does not always predict future performance. Economic influences, such as inflation or a recession, could skew the data being analyzed. Additionally, the way a company reports information may change over time. For example, there could be changes in where and when certain transactions are recorded, and this may not be immediately evident to financial statement users. It is also key to note that though all publicly traded companies in the United States are required to follow Generally Accepted Accounting Principles (GAAP) , there are many estimates and flexibility in how some standards are applied. This means that firms can still follow accounting standards appropriately but present some information differently from other firms.
It makes good sense for a company to use financial statement analysis to guide future operations so it can budget properly, control costs, increase revenues, and make long-term expenditure decisions. As long as stakeholders understand the limitations of financial statement analysis, it is a useful way to predict growth and financial strength.
Despite limitations, ratios are still a valuable tool if used appropriately. The next section discusses several operating efficiency ratios including accounts receivable turnover, total asset turnover, inventory turnover, and days’ sales in inventory. Operating efficiency ratios help users see how well management is using the financial assets of the firm.