Course Materials 

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Review

• SOS Math - Calculus

• ODE Cheat Sheet

• Review Topics for Exam I - Sample Exam

• Review Topics for Exam II - Sample Exam

• Review Topics for Exam III - Sample Exam

• Review Topics for Final Exam - Sample Final

First Order Equations

• Separable Equations

  • More on Separable Equations 2, 3

• Exact Differential Equations

• First Order Linear,

• Applications

• Integrating Factor

Maple and Other Software for ODEs

• Maple

  • Basic Maple (html, Maple File)

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

  • Maple Cheat Sheet (69 pgs)

• Using WolframAlpha

• Other Computer Algebra Systems

  • Maxima, (tutorial, Demos, Online),

  • Sagemath,

  • Others

• MATLAB

  • MATLAB direction fields

  • MATLAB Introduction

  • MATLAB Clone: Gnu Octave, Online

  • MATLAB and Simulink Cheat Sheets

• Solving ODEs

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

  • dsolve + ezplot example: EzplotExample.m

  • Maple, Sage, Mathematica, MS Excel, Python

  • GNU Octave - Differential Equations

  • Interactive Differential Equations

• See CODEE for more

• Desmos.com direction field, Differential equation

• Code for slope fields

• Apporto, UNCW New Virtual Desktop

Second Order Equations

• Second Order Differential Equations

• Examples

• Nonhomogeneous Equations

• Undetermined Coefficients

• Variation of Parameters

• Examples

• Cauchy-Euler
• SOS Math
• Notes

Simple and Forced Harmonic Motion

• The Simple Harmonic Oscillator - Desmos

• Simple Pendulum

• The Pendulum Lab

• Forced Harmonic Oscillator and Resonance

• Forced Harmonic Motion

• Visualizing Free and Forced Oscillations in Maple

• Tacoma Narrows Bridge Disaster

• Physics and Acoustics of Baseball and Softball Bats

Numerical Solutions

• Euler's Method Calculator, Geogebra Example

• Solving Differential Equations in MATLAB

• Learning Mathematics Using Maple - Videos

• Maple: Euler.mws

• MATLAB: EulerM.m, DEfield.m
• Simulink: EulerMethod.slx

Power Series Solutions

• Power Series Method - Lecture Notes in Wayback Machine

• Taylor.mws

• Desmos series plot

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

• Series Solutions and SOS Math

• Using Series to Solve Differential Equations
• Rainbows
• The Mathematics of Rainbows
• Notes on Airy Series
• Stokes's phenomenon: An asymptotic adventure
• Rainbow History I and Rainbow History II - Herman
• Airy Series - Maple
• SupernumeraryViolet.png and AiryStokesFringes.png - Figures
• MATLAB files: AiryVioletPurple.mlx, AiryColorMixing.mlx
• Special Series Solutions
• Legendre's equation
• Bessel Equations and Bessel Functions
• Hermite's equation
• Search for Laguerre, Chebyshev, Hypergeometric

Mathworld's Legendre Polynomials

• Mathworld's Bessel Functions and from efunda

• Frobenius Method

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

• Desmos ODE System Solver

• 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)

MATLAB and Simulink

• Simulink Computer Exercises and Printing Scope Plots

• MATLAB ODE Examples

• MATLAB Files

  • Solving ODEs in MATLAB pdf

  • Solve ODE and plot solution

  • Euler's Method

  • Quiverplot and Phaseportraits

• Simulink Files

  • First Order ODE

  • Constant Coefficient SOLDE

  • Cauchy-Euler Equation

  • Linear Systems, 2nd Example

  • Euler's Method

  • Harmonic Oscillator

  • Projectile Motion

  • Predator Prey