Math 235, Fall, 2011 Web Page

Lecture Notes

1. Introduction

2. First Order Linear Differential Equations and Bernoulli's Equation

2a. First Order Linear Differential Equations and Bernoulli's Equation--including hand-written notes

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

5. Exact Equations, Integrating Factors, and Homogeneous Equations

5a. Review for Exam-1

NOTE: Many of the remaining lecture notes will be changed during the course of the term. The current ones are left here to give an indication of the scope of the course.

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

8a. Examples of Complex Arithmetic

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

12baa. The Quick Method for Power Series recurrences at an ordinary point

12c. The Euler Equation

12d. Regular Singular Points and 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

18a. ---extra pages for section 18

18b-Graphing-Exercises

18b-Graphing-Exercises-Solutions

19. Higher dimensional linear homogeneous systems with constant coefficients

19a. Solving Cubic Equations--Nickalls

19b. Solving Cubic Equations--Holmes

20. Variation of Parameters for Systems

20a. Boundary Value and Eigenvalue Problems.

21. Partial Differential Equations -- the heat equation

21a. Some Examples of Heat Equation Problems

21b. Supplement to Heat Equation Notes

22. Periodic Functions and Fourier Series

22-Nov-29-2010. Expanded version of lecture given on Periodic Functions and Fourier Series

22a. Orthogonal Functions

22b. Some Fourier Series Problems

23. Review for Exam 3 and remaining course material