Course Materials 

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Texts

• Dr. Herman's Notes - Required Reading for this course
• LibreTexts Version of text
• Dr. Herman's MAT 361 Text and LibreTexts Version
• Solving Differential Equations Using Simulink
• A list of ODE texts

ODE Review

• Dr. Herman's MAT 361 Class
• Integrals you should know
• Old Midterm, Topics Review for Midterm
Final - Boundary Value Problem Review, More Problems
• ODE Cheat Sheet

History

• Genesis of Differential Equations
• Mathematicians 1550-1900
• Timeline - Mathematicians
• Timeline - Legal Paper
• Dr. Herman's History of Math notes
• Leibniz's 1684 paper and translation.
• Newton's classification of differential equations in terms of fluxions and fluents
• Euler's Institutionum calculi integralis, online and a translation.
• Boole's Differential Equations First Edition, 1859, 3rd Edition, 1872

Planar Systems

• Romance Maple File - Class Demo of Direction Fields
• Linear Systems
• Models of Species Interaction
• Visualizing Differential Equations
• 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 Wolfram Applet
• The Simple, but Nonlinear Pendulum Article
• Elliptic Integral of the First Kind -- from MathWorld
• Elliptic Functions

Applications

• Models of Love and Happiness
• Differential Equations Projects
• Nonlinear system project and Systems of Differential Equations
• SIMIODE Resources

Nonlinear Dynamics and Chaos

• Limit Cycle Maple Worksheet
• Plotting Nonautonomous Systems Maple File
• Duffing Equation Maple
• Maryland Chaos Group
• The Lorenz Attractor - in 3D

Boundary Value Problems

• Vibrating String & Separation of Variables

Fourier Series

• Introduction to Fourier Series
• Fourier Series - Eric Weinstein's World of Math
• Listen to Fourier Series and here too
• Maple Worksheet - fseries.mws, EvenOdd.mws
• 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
• Intermediate Methods of Mathematical Physics - J.J. Kelly

Special Functions

• Wolfram Function Site
• EqWorld - Mathematical Equations Page
• M. Abramowitz and I. A. Stegun Handbook of Mathematical Functions or PDF
• Classical Orthogonal Polynomials,
• Book by Vilmos Totik
• Schlömilch's Series.
• Applications
  • Coffee Cup Vibrations,
  • Dr. Herman's Vibrating Membranes
• Binomial Expansion, examples,
• Binomial coefficient
• Basic Hypergeometric Series and Applications

Green's Function

• George Green: Mathematician & Physicist, 1793-1841
• Green's Famous Essay

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)