Elementary Differential Equations
Chapter 1: First Order Equations
(Open for bug hunting)- Introduction
- Separable Equations
- Geometric Interpretation (Slope Fields)
- Exact Equations
- Numerical Methods
- Linear Equations
- Change of Variables
- Autonomous Equations
- Long Term Behavior and Population Models
- Theory of First Order Equations
- Optional: Calculus of Variations
- Homework Exercises
- Answers to the Odd Numbered Exercises
Interlude: Complex Variables
(Open for bug hunting)Chapter 2: Higher Order Linear Equations
(Open for bug hunting)- Theory of Linear Equations
- Homogeneous Equations
- Inhomogeneous Equations
- Variation of Parameters
- Numerical Methods for Higher-Order Equations
- Applications
- Exploring Spring-Mass Motions
- Homework Exercises
- Answers to Odd Numbered Exercises
Chapter 3: Laplace Transforms
(Under Construction)- Laplace Transforms
- Table of Laplace Transforms
- The Gamma Function
- Solving Differential Equations with Laplace Transforms
- Impulse Functions
- Convolutions
- Systems of Equations
- Non-linear Systems of Equations
- Geometric Methods for 2-dimensional Systems
- Homework Exercises
Chapter 4: Series Solutions
(Under Construction)- Power Series
- Series Solutions
- Radius of Convergence
- Euler Equations
- Regular Singular Points
- Series Solutions About Regular Singular Points
- Convergence of Series Solutions About Regular Singular Points
- Bessel Functions
- Where Do Variable Coefficient Problems Come From?
- Separation of Variables
- Boundary Value Problems
- Homework Exercises
Capstone to Calculus
(Under Construction)Please report any problems with this page to bennett@math.ksu.edu
©2010 Andrew G. Bennett