Course Materials 

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Review

• Integrals you should know

• 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, More examples here

• Applications

• Exact Differential Equations

• 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, Maxima in 10 min),

  • Sagemath,

  • Mathics,

  • Others

• MATLAB

  • MATLAB direction fields

  • MATLAB Tutorial

  • MATLAB Clone: Gnu Octave

  • MATLAB Cheet Sheets 1, 2

• Solving ODEs

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

  • dsolve + ezplot example: EzplotExample.m

  • MATLAB, Sage, Mathematica, MS Excel, Python

  • MATLAB and Octave tutorial

  Interactive Differential Equations

• See CODEE for more

• Desmos.com direction field

• Code for slope fields

Second Order Equations

• Second Order Differential Equations

• More Second Order ODEs

• 2nd Order, linear, homogeneous, const coeff

• Examples

Nonhomogeneous Equations

• Nonhomogeneous Equations

• Undetermined Coefficients and here

• Variation of Parameters and here

• Examples

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)

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