Math 235, Spring, 2009 Newhouse Class Notes

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.

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. Review for Exam-1

5b. 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

12a. Review of Sequences and Series

12b. 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

15e---Answers to Exam-3

16. Systems of Differential Equations

17. Linear Homogeneous Systems with Constant Coefficients

17-supplement. Some notes

17-supplement_2--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

23. Sample Problems for Exam 4

24. Solutions to Sample Problems for Exam 4

25. ---Answers to Exam-4

26. Sample Multiple Choice Final Exam ---Note: Unlike this sample, your Final Exam will have BOTH multiple choice problems and hand graded problems

27. Sample Multiple Choice Final Exam with Solution

28. The first two pages of the Final Exam--please read now and, when taking the exam, follow the instructions.

29. Room locations for the Final Exam--Please check your location BEFORE the exam date and arrive on time.

---Solutions to Final Exam