This page gives an approximate schedule of the topics and problems that will be covered in lecture (MWF) and recitation (TTh) respectively. Each homework set will be due in the recitation following the one in which the problems are covered. By "covered" we mean that you will have an opportunity to ask questions about that problem set. If there are no questions, then the TA will choose a selection of problems to work.
Suggestion: Work ahead. Read the related sections in the book. If you have looked at the section and the corresponding problems before the lecture, then you have two opportunities to ask questions (and at least a couple days) before the problem set is due.
M Aug 20 Overview
T 21 1.1 Some comments on modeling
Read 1.1;
Problems 1.1.3,8,9,11-13,20.
Read Lab 1.1
W 22 Modeling: variational ODE
Th 23 Try to understand the local behavior at
an equilibrium by
1. considering some explicit solutions and
2. using a numerical ode solver.
What can you say about the notion of uniqueness?
Find the Euler-Langrange equation associated to the
surface of revolution (about the x-axis) that passes
through two fixed points (a,f(a)) and (b,f(b)) and
has least area among such surfaces. (Hint the energy
functional in this case is just the area.) How is
this problem related to the shape of a hanging chain?
Find the Euler-Langrange equation of the
Brachistochrone. (See handout.)
Read 1.4.
F 24 1.4 Numerical approximations; Euler's method
CHECKLIST (Week 1)
M 27 1.2 Separable equations and mixing problems
Read 1.2 and make sure you understand the first three
sections absolutely perfectly.
T 28 1.4.5,6,10,11.
1.2.1,4,19,27,35,40.
W 29 1.3 Slope fields
Th 30 1.3.11,14-16.
1.4.19.
F 31 1.5 Existence and uniqueness.
1.5.5-8,14-18
CHECKLIST (Week 2)
M Sept 3 holiday
T 4 Read 1.6.
1.6.1,6,9
W 5 1.6 Phase space and linearization;
Limit sets for a single autonomous equation
Th 6 1.6.14,22,26,28.
F 7 Aside on second order linear equations (Phase space postponed)
1.6.34,35,36.
Read 3.6.
3.6.1,9,17-19,22 (In each problem, express the second order
ODE as an equivalent first order system.)
CHECKLIST (Week 3)
M 10 Single autonomous equation (continued)
T 11 Recitation canceled
W 12 Lecture canceled
Th 13 1.6.1,6,9,14,22,26,28.
F 14 Poincare' conjecture; 1.6 Linearization
CHECKLIST (Week 4)
M 17 Flows in phase space; Classification of equilibrium
Tu 18 (Go over the homework assigned above.)
W 19 Proof of the linearization theorem; 1.7 Bifurcations
Th 20 ??
F 21 Discussion of projects; Bifurcations (continued)
CHECKLIST (Week 5)
M 24 Bifurcations (continued)
T 25 1.7.4,5,13-15
W 26 Bifurcation theorem; Implicit Function Theorem
Th 27 1.8.7,21,22,24
1.9.3,8,11,23
F 28 1.8 First order linear equations
CHECKLIST (Week 6)
M Oct 1 2.1 First order systems; Vector fields
T 2 2.1.4,8,9,11,14,17,24.
W 3 2.2 Existence-uniqueness; Euler's method;
Dimensional considerations
Th 4 2.2.2,7,8,16,17,21-24,29
2.3.4,17,18
F 5 Exam 1.
CHECKLIST (Week 7)
M 8 Euler's method (continued) and the rest of Chapter 2
Limit sets; Poincare'-Bendixon Theorem (statement)
T 9 2.4.2,12,13,16
2.5,1,2,4,5
W 10 3.1 Linear planar systems with constant coefficients
(introduction)
Th 11 3.1.13,15,18,32,35
F 12 3.2 Linear planar systems (continued); changing basis
CHECKLIST (Week 8)
M 15 Fall Break
T 16 Fall Break
W 17 3.3 Linear systems (continued); two real eigenvectors
Th 18 3.2.8,12,17,19
3.3.6,10
F 19 3.4 Linear systems (continued); complex eigenvalues
CHECKLIST (Week 9)
M 22 3.6-7 Harmonic motion with linear damping;
second order equations
T 23 3.4.3-8,10,11,19,22
3.5.1-4,6,10,11
3.3.23-26
W 24 3.8 Higher dimensional systems; 4.1 Forcing
Th 25 3.8.6,14
4.1.4,18,28,34,40
F 26 4.2-3 Periodic forcing and resonance
CHECKLIST (Week 10)
M 29 4.2-3 Periodic forcing and resonance
T 30 4.2.16-19,22
4.3.6,8,18,22
W 31 Comments on Fourier series
Th Nov 1
F 2 6.1 Laplace Transforms
CHECKLIST (Week 11)
M 5 Exam 2
T 6
W 7
Th 8
F 9
CHECKLIST (Week 12)
M 12 6.2-3 Laplace Transforms
T 13 6.1.5,6,14,21-27
W 14 6.3 (continued)
Th 15 6.2.2,3,14-16,19,20
6.3.7,15-21,27-30,36.
F 16 6.4 Introduction to Distributions
CHECKLIST (Week 13)
M 19 Worksheet on Laplace Transforms
T 20 ?
W 21 Explanation of worksheet
Th 22 Thanksgiving Holiday
F 23 Nobody would come anyway day
CHECKLIST (Week 14)
M 26 The Dirac-Delta
T 27 6.4.1,2,6
W 28 Distributions (conclusion)
Th 29 ?
F 30 Roberto Lopez: Deflating Soap Bubbles
CHECKLIST (Week 15)
M 3 Nonlinear Systems I (5.1 Linearization)
Nonlinear Systems II (5.3 Hamiltonian Systems)
T 4 5.1.4,5,18,19
5.2.1-3
W 5 Projects/Review ?
Th 6 5.3.2,4-8
F 7 Review
CHECKLIST (Week 16)