This page should be consulted frequently, since the syllabus and dates for tests may be adjusted throughout the semester.

If you are reading a printed page instead of browsing, please note that there are several links below, so you should actually browse!

There are additional notes, found here, on the following topics:

  • N1 = modeling
  • N2 = bifurcations
  • N3 = phase plane analysis
  • N4 = matrix exponentials
Some of these notes contain homework problems, which are indicated as "N1", etc, in the syllabus.

You are responsible for all assigned problems; quizzes will be based on these assigned problems. Make sure that you understand the solutions to all of them!
 
 

Sections Subjects Assignments Notes
1 N1 Modeling N1: all (answers)
2 1.1, 1.2 Modeling & Separation of Vars, ctd 1.1:1,3,5,9  1.2:1,3,7,13,25,29,31,35
3 1.1, 1.2 Modeling & Separation of Vars, ctd
4 1.3 Slope Fields 1.3:1,3,7,9,11,13,15,17 a
5 1.4,1.5,1.6 Euler; Existence, Equilibria, Phase Line 1.4:1,11,13  1.5:1,3,10  1.6:1,3,5,7,9,11,17,19,21,25,31,35
6 N2, 1.7 Bifurcations 1.7: 1,3,5,7,17,19
7 1.8 Linear Differential Equations 1.8: 1,3,5,7,9.11.13,23
8 2.1 Systems 2.1: 1,2,7,8,9,17,19,21,23,25,26,27,29 d
9 2.2 Geometry of Systems 2.2: 1,3,5,7,9,11,13,1517,21,23,25,27,29 a
10 2.3, 2.4 Analytic Methods, Euler's Method 2.3: 1,3,5,7,9,11,19 2.4: 1,3,5,14,15 e
11 N3 Phase Plane N3: all (answers)
12 exam 1 Through 2.2 included
13 3.1, N4 Linear Systems, Matrix Exponentials 3.1: 1,3,5,7,9,13,17,19,21,27,29,33,35 f
14 N4 Matrix Exponentials, ctd N4: all (answers)
15 3.2 Straight-Line Solutions 3.2: all odd 1-19
16 3.3 Phase Plane: Real 3.3: all odd 1-15
17 3.4 Phase plane: Complex 3.4: all odd 1-15,19,21,23
18 3.5 Repeated & Zero Eigens 3.5: all odd 1-17 g
19 3.7 Bifurcations 3.7: parts "c" of: 3,7,11,13
20 3.6 Second-Order Linear 3.6: all odd 1-17,22(a,b) h
21 3.8 3-Dim Linear 3.8: 4,5,6,7
22 4.1,4.2 Forced Harmonic; Sinusoidal Forcing 4.1: 1,3,7,11,17,19,23,25,29,31,33,35,37,39  4.2: odd 1-13,16-19,23  
23 exam 2 2.3/3.7 (lectures 10/20)
24 4.4 Steady State 4.4: see note i below i
25 4.3 Resonance 4.3: all odd 1-13, all 15-18
26 5.1 Equilibria, Linearization 5.1: all odd 1-17, except 5
27 8.1 Discrete Systems 8.1: 1,3,5,7,9,15,19,23,27,31
28 8.2 Fixed/Periodic points 8.2: 1,7,9,13,15
29 final exam all material covered during the semester

Notes:

a. Please use either Maple or the phase plane grapher in the main 252 page for section 1.3 and 2.2 problems involving slope and vector fields.

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

e. The material on damped harmonic oscillator does not fit well with the topic of section 2.3, and will be left for later.

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. Sec 3.7: We will not  cover the description of the trace-det plane as the book does. (On the other hand, we did see already in class that
       charpoly(A)  =  x2 - trace(A) x + det(A) ,
so we already know that the eigens depend on tr and det.  In any case, it is a good idea to read this section from the book - it is very nice!)
What we will  do here is to study one-parameter families of 2-dim linear systems.  A typical problem is: for a given family, find the bifurcation parameters, and draw a sketch of the phase plane for parameter values near the bifurcation values.

h: Problem 22(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!

i: 4:4: for each of the odd problems 4.2:1-9, write the steady-state solution in the form   A cos(wt+f)
 

back to the 252 page


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