Math 235, Fall, 2010 Web Page

Some Maxima resources for ODE's:

1. The following link is the main web page for Maxima, a very useful software system for mathematics.

2. See the documentation page for tutorials.

3. I mainly use Xmaxima, which has a nice tool "plotdf" for plotting direction fields of differential equations.

Complete Set of Lecture Notes (around 23 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. For example, do a search for "integration by parts" or "partial fractions".

4. Some applications of first order differential equations

4a. Corrections and supplement to Section 4 on some applications of first order differential equations

5. Exact Equations, Integrating Factors, and Homogeneous Equations

5a. Review for Exam-1

5b. Solutions for Exam-1

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

10w1. Particular Solutions-Variation of Parameters (additional written lecture-1)

10w2. Particular Solutions-Variation of Parameters (additional written lecture-2)

11. Some applications of second order differential equations

11a. Mark Ketchum's Bridge Collapse Page--Resonance in Action!

12. Forced Oscillations

12a. Review of Sequences and Series

12b. Series solutions for Linear Second Order Equations near an ordinary point

12ba. Supplement to Series solutions for Linear Second Order Equations near an ordinary point

12c. The Euler Equation

12d. Regular Singular Points

12e. The Frobenius Method

13. Laplace Transform

13a. Additional Lecture Content for Laplace Transform

14. Initial Value Problems and the Laplace Transform

14a. Heaviside functions and piecewise continuous maps

14b. 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

16. Systems of Differential Equations

16-R More details on matrices and systems of linear equations.

17. Linear Homogeneous Systems with Constant Coefficients

17-Nov_9_2010. General Description of two dimensional linear systems

17-supplement-1 Section 17 with some additional notes.

17-supplement-2. Some notes

17-supplement-3--WebWork sample problems for problem set 15. Some notes

17-a Systems of Linear Equations.

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

20a. Boundary Value Problems

21. Partial Differential Equations -- the heat equation

21a. Some Examples of Heat Equation Problems

22. Periodic Functions and Fourier Series

22a. Orthogonal Functions

22b. Some Fourier Series Problems