## Math 235, Fall, 2016 Web Page

Syllabus for Fall, 2016

Class Web Site For Course Notes, Exam information, etc.

Note: The notes below are informal notes which are to be corrected and updated regularly.

### Lecture Notes

1. Introduction
2. First Order Linear Differential Equations and Bernoulli's 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. Some Worked Homework Problems on Applications (by J. Bohn)
4b. Some Worked Homework Problems on Applications (by X. Hu) )
4c. Some Worked Homework Problems on Applications (by R. Zhang)
5. Exact Equations, Integrating Factors, and Homogeneous Equations
5a. Some Additional Examples of Exact Equations and Integrating Factors
5-R. Review 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
8a. Examples of Complex Arithmetic
9. Particular Solutions-Undetermined Coefficients
10. Particular Solutions-Variation of Parameters
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
12c. The Euler Equation
12d. Regular Singular Points and the Frobenius Method
13. Laplace Transform
13a. Laplace Transform--General Properties Summary
14. Initial Value Problems and the Laplace Transform
14b. A supplemental Laplace Transform Table
15. Step Functions and initial value problems with discontinuous forcing
15aa. Delta Function Heuristics
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 Linear Equations
16a. Systems of Linear Equations with supplemental handwritten notes
17. Systems of Differential Equations and Linear Homogeneous Systems with Constant Coefficients
17a. Supplement to Section 17
17b. First and Second Fundamental Solutions
18. Geometry of two dimensional Linear Homogeneous Systems with Constant Coefficients
18a. ---extra pages for section 18
19. High Dimensional Linear Homogeneous Systems
20. Variation of Parameters for Systems
21. Boundary Value Problems
21a. Some Boundary Value Problems and Solutions
22. Fourier Series and Periodic Functions
23. Partial Differential Equations, Separation of Variables, and the Heat Equation
23a. Supplement to Heat Equation