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
• Exam Review
• Review I, Sample Exam I
• Review II, Sample Exam II
• ODE Cheat Sheet
• Videos: Variation of Parameters, Cauchy-Euler Equations,Reduction of Order, and Method of Undetermined Coefficients and Modified Undetermined Coefficients

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
• Direction field plotter, GeoGebra Example
• Maple Files: Wiffle Ball, Linear Systems
• Exponentiating a matrix
• Matrix Exponentials, Student Version
• The Matrix Exponential via Eigenvalues and Eigenvectors
• Putzer’s Algorithm for e^At via the Laplace Transform, JSTOR
• Jordan Canonical Form
• Putzer Matrix Exponential Formula for 2x2 Matrices
• Why should you calculate the Jordan normal form anyway? blog
• Avoiding the Jordan Canonical Form in the Discussion of Linear Systems with Constant Coefficients, at MAA by Putzer

Nonlinear Systems

• Bifurcations in Maple - HTML
• Phase Plane for Simple Systems - Maple
• Class Examples - Maple, MATLAB, Simulink
• Nonlinear System Example 1 Maple file
• ODE plots - Live Script ODEplots.mlx
• ODE system ODEsys.mlx
• Simulink - 2nd Order ODE NewSOLDE.slx
• Simulink - Nonlinear Pendulum NonlinearPendulum.slx
• Simulink - A system of ODEs QuickDirtySystem.slx
• See Solving Differential Equations Using Simulink for more.
• Video for ODEs in Simulink
• Nonlinear Pendulum Wolfram Applet
• The Simple, but Nonlinear Pendulum Article
• Exact solution for the nonlinear pendulum Article
• Elliptic Integral of the First Kind -- from MathWorld
• Elliptic Functions
• The Poincare´-Bendixon theorem PDF

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

Software for ODEs

• Numerical ODEs- R.L. Herman Notes

• Maple

  • Basic Maple (html, Maple File)

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

  • Maple Cheat Sheet (69 pgs)

• Wolfram Mathematica ODEs

• Using WolframAlpha - Dr. Herman's List

• Other Computer Algebra Systems

  • Maxima, (tutorial, Maxima in 10 min),

  • Sagemath, free open source alternative to Magma, Maple, Mathematica and Matlab.

  • Mathics, Mathematica clone using Python.

  • Others like Scilab (and Xcos), Reduce

  • Solving Differential Equations in R and ODE with R

• MATLAB

  • MATLAB direction fields

  • MATLAB Tutorial

  • MATLAB Clone: Gnu Octave

  • MATLAB Cheat Sheets: Official one
    Notre Dame Plot Cheatsheet, MIT and MathWorks in different languages

• MATLAB ODE Examples

• MATLAB Files

  • Solving ODEs in MATLAB pdf

  • Solve ODE and plot solution

  • Euler's Method

  • Quiverplot and Phaseportraits

• Simulink
• Solving Differential Equations Using Simulink - by Dr. Herman

• Simulink Computer Exercises and Printing Scope Plots

• Simulink Files

  • First Order ODE

  • Constant Coefficient SOLDE

  • Cauchy-Euler Equation

  • Linear Systems, 2nd Example

  • Euler's Method

  • Harmonic Oscillator

  • Projectile Motion

  • Predator Prey

• Simulink Alternatives: Xcos, Pictorus, Collimator

• Solving ODEs

  • Direction field example, dfield.m, plus ode45, dfield2.m + func.m

  • dsolve + ezplot example: EzplotExample.m

  • MATLAB, Sage, Mathematica, MS Excel, Python

  • Interactive Differential Equations

  • See CODEE for more

  • Desmos.com direction field

  • Assorted Codes for slope fields

Maple Worksheets (Old)

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)