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
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) = x^{2}
- 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)