Class Handouts:

The following files are in .pdf format.

  • The Greek Alphabet

  • Aide Memoire

  • Guidelines for Partial Fractions

  • Some Useful Trigonometric Identities

  • Common Notation

  • Table of Elementary Laplace Transforms

  • Routine Exercises for Laplace Transforms

  • Some Facts about the Gamma Function

  • Answers to Homework 1

  • An Example of the Convolution Theorem

  • Notes on Cramer's Rule

  • Solving Linear Systems with Laplace Transforms

  • Another Example for Systems

  • Differential Equations with Variable Coefficients

  • An Example of a Volterra Equation Model

  • Simple Two-Point Boundary Value Problems

  • An Important Laplace Transform

  • Laplace Transform for Periodic Functions

  • Answers to Homework 2

  • Answers to Homework 3

  • Elementary Z-transforms

  • Simple Properties of Z-transform

  • Answers to Hour Exam I

  • Axioms for a General Vector Space

  • Proofs of some Arithmetic Facts

  • Dot Products and Norms

  • Answers to Homework 5

  • Guidelines for Systems

  • Systems with Distinct Real Eigenvalues

  • Systems with Complex Conjugate Eigenvalues

  • Systems with Repeated Real Eigenvalues

  • Another Example with Complex Eigenvalues

  • Computation for the Double Root Case