Course Materials 

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Texts

• Dr. Herman's Notes - Required Reading for this course
• A list of ODE texts

ODE Review

• Dr. Herman's MAT 361 Class

• Integrals you should know

• SOS Math ODEs

• Old Midterm, Topics Review for Midterm

• Notes from 2007 Review Session #1

• Final - Boundary Value Problem Review, More Problems

Planar Systems

• Romance Maple File <== Class Demo of Direction Fields
• Linear Systems - SOS Math
• More Linear Systems
• Eigenvalues and Eigenvectors - SOS Math
• Qualitative Analysis - SOS Math
• Phase Portraits - Applet or try a Mathlet
• Models of Species Interaction
• Interactive Differential Equations

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

• Mass-Spring-Dashpot Animation in Maple

Nonlinear Systems

• Bifurcations in Maple - HTML
• Phase Plane for Simple Systems - Maple
• Nonlinear Pendulum Applet
• The Simple, but Nonlinear Pendulum Article
• A Nonlinear Pendulum Project
• Nonlinear Differential Equations PPT Lecture
• Elliptic Integral of the First Kind -- from MathWorld
• Elliptic Functions
• Lotka-Volterra Tool
• Population Dynamics in Java
• A Lotka-Volterra Three-species Food Chain

Applications

• Models of Love and Happiness

Nonlinear Dynamics and Chaos

• Limit Cylce Worksheet
• Plotting Nonautonomous Systems Maple File
• Duffing Equation Maple
• Nice Dynamical Systems Example
• Poincare-Bendixon Theorem Summary Poster, More on Limit Cycles
• Nonlinear Systems and Control
• Double Pendulum and other dynamics
• Duffing Equation Applet
• Duffing Circuit
• Maryland Chaos Group
• The Lorenz Attractor - in 3D
• Quantum Chaos

Boundary Value Problems

• Vibrating String & Separation of Variables
• Numerical Solution of BVPs
• Solution of Heat Equation

Fourier Series

• Introduction to Fourier Series

• Special Trigonometric Bases - Harvey Mudd College

• Products of Trigonometric Functions, also at ThinkQuest

• Fourier Series - Eric Weinstein's World of Math

• SOS Math - Fourier Series

• Listen to Fourier Series

• Fourier Series and Waves Example profiles

• Maple Worksheet - fseries.mws, EvenOdd.mws

• Convergence of Fourier Series and at SOS Math

• Properties needed in convergence proof

• Article on Convergence

• See Fourier Series on YouTube and Gibbs Phenomena or Videos on Fourier Series - Donny Lee

• Mobius Transformations Revealed on YouTube

Sturm-Liouville Theory

• Efunda Definition
• Theory, Summary
• Sturm-Liouville Systems
• Adjoint Operator Notes
• Applied Math Notes
• Intermediate Methods of Mathematical Physics - J.J. Kelly
• Orthogonality
• Properties, etc.

Special Functions

• Wolfram Function Site
• EqWorld - Mathematical Equations Page
• M. Abramowitz and I. A. Stegun Handbook of Mathematical Functions
• Classical Orthogonal Polynomials,
• Book by Vilmos Totik
• Legendre Functions, Summary
• Spherical Harmonics
• Bessel Functions, Summary
• Fourier Bessel Series, Convergence and here
• Schlömilch's Series.
• Applications
  • Coffee Cup Oscillations,
  • Dr. Herman's Vibrating Membranes
  • Bessel Functions and a Vibrating Drum
• Binomial Expansion, examples, and this one!
• Binomial coefficient
• Basic Hypergeometric Series and Applications

Green's Function

• George Green: Mathematician & Physicist, 1793-1841

• Green's Famous Essay

• Method of Variation of Parameters

Review topics are posted: BVP_Review.doc or in PDF

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)

• Slope Fields in Maple (html, Maple File)

• Bifurcations in Maple (html, Maple File)

• Linear Systems (Maple File)

• Laplace Transforms (Maple File)

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