Course Materials 

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Review

• Integrals you should know

• SOS Math - Calculus

• Review for Exam I

• Review for Exam II

Introduction

• View Video Lecture 1

• History Lecture

First Order Equations

• Separable Equations

  • More on Separable Equations 1, 2, 3

• Exact Differential Equations

• First Order Linear

  • More - 1, 2, 3

• Applications

• Autonomous Equations

• Bifurcations in Maple (html, Maple File)

• Another Set of Lectures

Maple and Other Software for ODEs

• Basic Maple (html, Maple File)

• Maple Operations for ODEs I (html, Maple File)

• Interactive Differential Equations

Second Order Equations

• Second Order Differential Equations

• Analytical Methods for Second Order Linear Ordinary Differential ... and Examples

• Homogeneous, Constant Coefficient Equations Video

• Linear Dependence and the Wronskian Video

• Read Kutz pgs 16-24.

• More Second Order ODEs

• Second Order Equations from Queensland

Nonhomogeneous Equations

• Road Map with Links

• Method of Undetermined Coefficients, and More

• Variation of Parameters Formula

• More on Variation of Parameters

• Theoretical Description of Spacecraft Flybys by Variation of ...

• Examples

  • Undetermined Coefficients

  • Variation of Parameters

Simple and Forced Harmonic Motion

• The Simple Harmonic Oscillator

• Simple Pendulum

• The Pendulum Lab

• Notes on the Forced Harmonic Oscillator (PDF)

• Forced Harmonic Motion

• Visualizing Free and Forced Oscillations in Maple

• Video Lecture 8

• Tacoma Narrows Bridge Disaster

• Physics and Acoustics of Baseball and Softball Bats

Numerical Solutions

• Euler's Method Applet, Another One

• Matlab in DEs

• Maple File Euler.mws

Power Series Solutions

• Power Series Method - Lecture Notes from James Cook University READ!

• Taylor Series Applet, Taylor.mws

• Nice Taylor Polynomial Plotter

• Taylor Series - Why We Want Them and How We Find Them

• Power Series Section from Larson Calculus text - includes problems!

• More on Power Series Solutions - More Examples and Problems

Cauchy-Euler Equations

• SOS Math

• Recipe - PDF - Order 2, PDF File 2, Problems and Solutions!

Special Functions

• Mathworld's Legendre Polynomials

• A Study of the Legendre Functions

• Legendre Applet

• Frobenius Method 1, 2, 3

• Mathworld's Bessel Functions and from efunda

• Essentials of Bessel Functions

Laplace Transforms

• Laplace Transform Table - MS Word

• Practice Laplace Transform Problems

• Introduction to Laplace Transforms for Engineers
• Mathworld
• Dirac Delta Function - Mathworld, K. Bryan's The Delta Function
• Tables
  • Collections of Worksheets! http://www.equationsheet.com/ 
  • http://www.vibrationdata.com/Laplace.htm 
  • eFunda: Laplace Transform Table
  • http://cnyack.homestead.com/files/alaplace/laptre.htm 
  • Table of Laplace Transform Properties 
  • http://www.sosmath.com/tables/laplace/laplace.html 
• Examples

Systems of Differential Equations

• Romance Maple File <== Class Demo of Direction Fields
• Linear Systems - SOS Math
• Eigenvalues and Eigenvectors - SOS Math
• Qualitative Analysis - SOS Math
• Phase Portraits - Applet or try a Mathlet
• First Order Systems - Lecture notes on matrix methods in PDF
• Models of Species Interaction
• Interactive Differential Equations

• Solving Linear Systems - Summary of Matrix Methods - R. Herman

Maple Worksheets 

Note: Worksheets are in Maple 8 files and need the software to run. Views of the worksheets are provided as webpages (html) which do not need Maple.

• Basic Maple (html, Maple File)

• Getting Started with Differential Equations in Maple

• Slope Fields in Maple (html, Maple File)

• Bifurcations in Maple (html, Maple File)

• Linear Systems (Maple File)

• Laplace Transforms (Maple File)