A (Not Really) Complex Method for Finding Solutions to Linear Differential Equations (UMAP)

A unit using a method to find solutions to linear differential equations. By completion of this module students will be able to understand and use the complex method to find a particular solution to linear differential equations with constant coefficients.

Table of Contents:

1. INTRODUCTION
1.1 The Purpose of this Module
1.2 Terminology

2. THE COMPLEX METHOD
2.1 Discussion of the Method
2.2 Theoretical Statement of the Method
2.3 Illustrations

3. HOW TO HANDLE NONHOMOGENEOUS PARTS INVOLVING K cos ß t, K sin ßt
3.1 Euler's Identity
3.2 Illustrations and Further Explanation
3.3 Further Extension

4. A FINAL EXTENSION OF THE COMPLEX METHOD
4.1 The Nonhomogeneous Part as a Linear Combination

5. UNIT EXAM

6. ANSWERS TO EXERCISES

7. ANSWERS TO UNIT EXAM

8. APPENDIX