This syllabus is intended as a general outline of the course. It was originally written by E. Sontag for the first edition of the text and adapted to the second edition by R. Wheeden. Individual insturctors may alter its pace, assign different homework, and add or delete topics. Some variations will be described briefly in the notes following the syllabus.

Assignments usually refer to sections of the textbook. A designation such as N4 is a link to a supplementary note.

 
 

#	Sections	Subjects	Assignments	Notes
1	N1	Modeling	all (answers)
2	1.1	Modeling (continued)	1, 3, 5, 9.
	1.2	Modeling & Separation of Vars	1, 3, 7, 13.
3	1.2	Separation of Vars (continued)	25, 29, 31, 35.
4	1.3	Slope Fields	1, 3, 7, 9, 11, 13, 14, 15, 17.	a
5	1.4	Euler's Method	1, 11, 13.
	1.5	Existence and Uniqueness	1, 3, 10.	b
	1.6	Equilibria and Phase Line	1, 3, 5, 7, 13, 15, 23, 25, 27, 31, 37, 43.
6	N2	Bifurcations	(No exercises in N2)
	1.7		1, 3, 5, 9, 21, 23.
7	1.8	Linear Differential Equations	1, 3, 5, 7, 9, 11, 13, 25.
8	2.1	Modelling via Systems	1, 2, 7, 8, 9, 17, 19, 21, 23, 25, 26, 27, 29.	c
9	2.2	Geometry of Systems	1, 3, 5, 7, 9, 11a, 13, 15, 17, 19, 21, 23, 25, 27.	a
10	2.3	Analytic Methods	1, 3, 5, 7, 9, 11, 19.	d
	2.4	Euler's Method	1, 3, 5, 14, 15.
11	N3	Phase Plane	all (answers)	e
12	exam 1		Through 2.2 included
13	3.1	Linear Systems	1, 3, 5, 7, 9, 13, 17, 19, 21, 27, 29, 33, 35	f
	N4	Matrix Exponentials		g
14	N4	Matrix Exponentials (continued)	all (answers)	g
15	3.2	Straight-Line Solutions	all odd 1-19
16	3.3	Phase Plane: Real Eigenvalues	all odd 1-15.
17	3.4	Phase plane: Complex Eigenvalues	all odd 1-15, 19, 21, 23.
18	3.5	Repeated and Zero Eigenvalues	all odd 1-17.
19	3.7	The Trace-Determinant Plane (emphasizing one-parameter families)	parts "c" of: 3, 7, 11, 13.	h
20	3.6	Second-Order Linear	all odd 13-29; 36(a,b).	h,i
21	3.8	3-Dim Linear	4, 5, 6, 7.
22	4.1	Forced Harmonic Oscillators	1, 3, 5, 7, 9, 13, 19, 21, 25, 27, 31, 33, 35, 37, 39, 41.
	4.2	Sinusoidal Forcing	odd 1-13, 16-19, 23
23	exam 2		2.3/3.7 (lectures 10/20)
24	4.4	Steady State	Special exercises.	j
25	4.3	Resonance	all odd 1-17, all 20-23
26	5.1	Equilibria, Linearization	all odd 1-17, except 5.	h
27	8.1	Discrete Systems	1, 3, 5, 7, 9, 15, 19, 23, 27, 31.
28	8.2	Fixed/Periodic points	1, 7, 9, 13, 15.	k
29	final exam		all material covered during the semester

Notes:

a. Please use either Maple or the phase plane grapher for section 1.3 and 2.2 problems involving slope and vector fields.

b. The existence and uniqueness theorem may be applied in abutting regions with continuity across the boundary to allow for piecewise continuous forcing functions.  Projects exploring this have been used in the course.

c. Sections 2.1/2.2 are not really different, and should studied (and possibly lectured upon) simultaneously.  Even 2.3 and 2.4 are not very different, actually.

d. The material on damped harmonic oscillator does not fit well with the topic of section 2.3, and may be deferred until the topic is considered in more detail in chapter 4.

e. Instead of the emphasis on exact trajectories in N3 and related supplements, instructors may introduce isoclines at this point to help guess phase plane portaits in simple cases like saddle points. The aim should be to complement the study of straight line solutions to appear in section 3.2 rather than to insert all of section 5.2 into the syllabus at this point.

f. Note to students: please make sure to review eigenvalues and eigenvectors from your linear algebra notes (which you kept from when you took the course!)

g. Some instructors may wish to skip the notes N4. The matrix exponential, while a useful topic (developed further in notes elaborating on the case of complex eigenvalues) , may be omitted. The time saved could be used to introduce variation of parameters.

h. Instructors may wish to introduce some or all of section 5.1 when discussing sections 3.6 and 3.7. Students should notice that phase planes for linear systems help predict those for nonlinear ones. Section 5.1 is an important part of the course; if it is not introduced in connection with sections 3.6 and 3.7, instructors should be sure to give adequate coverage later.

i. Problem 36(c) is worth looking at - the design of active automobile suspension systems is an area of much current research (at places like Ford, for example) - this question can be taken as an open ended one - be creative, and perhaps introduce nonlinear damping and nonlinear springs!

j. The exercises for 4.4 are to write the steady-state solution of the odd problems 1-9 of section 4.2 in the form   A cos(wt+f).

k. Instructors emphasizing bifurcations should aim to allow more time for chapter 8 in order to include sections 8.3 and possibly also 8.4.
 

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Last updated: June 28, 2002