Math 235, Fall-2004, Newhouse Class Notes

Section 001 syllabus
Section 003 syllabus
Some important dates
Note: These are informal notes which are to be corrected and updated regularly.

Some Mathematica resources for ODE's:

1. The following link is the main web page for a very nice book written a few years ago by Gray-Mezzino-Pinsky. As far as I know, the book is no longer in print (a shame!). While the packages were written for Mathematica versions 2 and 3, I find that, except for minor errors, the main package works with versions 4.1 and 4.2, as well. It probably also works with version 5.

2. Here is a cumbersome way to use the main package "ode.m" in MS Windows.

3. A basic Mathematica Tutorial: From Kit Dodson's page

Some Videos

Lecture Notes - Complete Set -- 10.2 MB

Lecture Notes

1. Introduction
2. First Order Linear Differential Equations
2a. Bernoulli's Differential Equation
3. Separable Differential Equations and some differences between linear and non-linear equations
Note that various techniques of integration are useful for solving separable equations. The Web has many useful resources to aid in learning and reviewing some of those techniques. Look at the following links for nice reviews of Integration and Partial Fractions.
4. Some applications of first order differential equations
5. Exact Equations, Integrating Factors, and Homogeneous Equations
5a. Exam-1 with answers
6. Linear Differential Equations of the Second Order--general properties and constant coefficients
7. Some special second order differential equations
8. Reduction of Order and more on complex roots
9. Particular Solutions-Undetermined Coefficients
10. Particular Solutions-Variation of Parameters
10a. Exam-2 with answers
11. Some applications of second order differential equations
Solution to problem 11, page 202, Boyce-DiPrima, 8th edition.
Some links on resonance
breaking a glass --physics USC
Mark Ketchum's Bridge Collapse Page
12. Forced Oscillations
13. Laplace Transform
14. Initial Value Problems and the Laplace Transform
14a. A supplemental Laplace Transform Table
15. Step Functions and initial value problems with discontinuous forcing
15a. Some Solutions of Problems using Laplace Transforms--1
15b. Some Solutions of Problems using Laplace Transforms--2
15c. Some Solutions of Problems using Laplace Transforms--3
15d. Some Solutions of Problems using Laplace Transforms--4
15e---Exam-3
15f---Answers to Exam-3
16. Systems of Differential Equations
17. Linear Homogeneous Systems with Constant Coefficients
17-supplement. Some notes
18. Geometry of two dimensional Linear Homogeneous Systems with Constant Coefficients
---extra pages for section 18
19. Higher dimensional linear homogeneous systems with constant coefficients
20. Variation of Parameters for Systems
21. Partial Differential Equations -- the heat equation
21a. Some Examples of Heat Equation Problems
22. Periodic Functions and Fourier Series
23. Sample Problems for Exam 4
24. Solutions to Sample Problems for Exam 4
25. ---Answers to Exam-4
---Solutions to Final Exam

Exercises