Course Materials

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Exam I Review - PDF
Exam II Review - PDF
2012 Exams - I, II, III
Sample Final, Review Topics
Spherical Harmonics

Dimensional Analysis

• Dimensional Analysis
• Blast Wave
• Buckingham Pi Theorem, Hanche-Olsen, Order of Magnitude Physics (Postscript), Examples

Mathematics Background

• Integrals you should know (MS Word)

• SOS Math - Calculus

• Summary Sheet on Exponential and Logarithms (MS Word)
• Summary of Basic Derivatives and Integrals (MS Word)
• Integration by Substitution (Visual Calculus)
• Integration by parts - SOS Math, Examples, Visual Calculus
• Improper Integrals - SOS Math,
• The Wolfram Integrator, http://www.wolframalpha.com/
  • Examples for WolframAlpha

Differential Equations

• Separable Equations

  • More on Separable Equations 1, 2, 3

• First Order Linear

  • More - 1, 2, 3

• First Order Applications

• Speed of a Sky Diver
• Surviving Free Fall?

• Second Order Differential Equations

• More Second Order ODEs

• Method of Undetermined Coefficients

• Variation of Parameters

Simple and Forced Harmonic Motion

• The Simple Harmonic Oscillator

• Simple Pendulum

• The Pendulum Lab

• Forced Harmonic Motion

• Tacoma Narrows Bridge Disaster

• Physics and Acoustics of Baseball and Softball Bats

Systems of Differential Equations

• Linear Systems - SOS Math
• More Linear Systems
• Eigenvalues and Eigenvectors - SOS Math
• Qualitative Analysis - SOS Math
• Mathlet
• Models of Species Interaction
• Interactive Differential Equations

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

• Mass-Spring-Dashpot Animation in Maple

• Maple Examples

Wolfram Alpha - an alternative to Maple checking and more

• Fourier series

  • plot sum_(k=1)^10(4/pi sin((2 k-1)*x)/(2 k-1))

  • plot sum_(k=1)^10(4/pi sin((2 k-1)*x)/(2 k-1)) x=0 to 2 pi

  • plot sum_(n=1)^10(cos(2 n pi x)/(n pi)^2- sin(2 n pi x)/(n pi)) x=0 to 4

  • plot sum_(k=1)^10(2/pi^2 cos(2(2 k-1)*pi*x)/(2 k-1)^2)

• Maple Version: plot(1/4+sum((cos(n*Pi)-1)/(n*Pi)^2*cos(2*n*Pi*x),n=1..100),x=-1..2);

• What is Wolfram Alpha?

  • Ask Wolfram - Part 1, Part 2

  • Info for Calculus Students

  • Learn by Examples ... see physics section

• Fourier Series Maple Plots - HW #6

Select Videos

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

• Dr. Tisdell - Intro to Fourier Series and more including
  Separation of Variables for PDEs

• MATLAB for Beginners Part 1 - and see others

• Maple: State-of-the-Art Visualization Capabilities

• Walter Lewin - Derivation of Wave Equation

• Fourier Transform Film, I will derive, Tom Lehrer New Math - songs in YouTube about math

• A Crash Course in Contour Integration

• Mobius Transformations Revealed

• The Fourier Transforms and its Applications

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