Syllabus for Fall, 2016

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

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

- 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