Course Materials 

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Programming

Basics

• Maple Basics: HTML, Basic.mws (Release 5.1)
• Mathcad Basics: HTML, Basics.mcd (Version 6.0)
• MATLAB Basics: HTML
• Using MATLAB

  • A Matlab Tutorial

  • Octave - Open Source Software that recognizes many Matlab functions

  • Matlab Educational Demos

  • Introduction to Computer Programming with MATLAB

  • Online Tutorial

  • Creating a GUI in Matlab 5

  • Matlab Training Sessions

• Peter Stone's Maple Worksheets

Finding Roots

• Bisection Method
  • Class Example in Matlab: bisect.m, func.m
• Fixed Point Iteration
  • Fixed Point Applet
  • Matlab: fixedpt.m, func2.m
• Newton's Method
  • Matlab: newton.m, func.m, dfunc.m
  • MathCAD: newton.mcd
• Secant Method
  • Matlab: secant.m
• Several Methods in Maple: roots.mws

Interpolation

• Lagrange Interpolation - Math World
• Applet with draggable points
• Using Maple for Lagrange Interpolation Maple 8 File
• Mathcad: interp.mcd
• Pade Approximations
• Matlab Files For Interpolation and Associated Plotting Routines
  • Lagrange Interpolation interpL.m , plotinterpL.m
  • Lagrange Interpolation done piecewise interpL2.m, plotinterpL2.m, points.m
  • Neville's Method nevilleQ.m, plotneville.m
  • Divided Differences divdiff.m, ddfun, plotdivdiff.m
  • Hermite Interpolation hermite.m, hermfun.m, plothermite.m
• Matlab Help
  • Interpolation (1d)
  • Cubic Spline Example

Numerical Differentiation

• Maple Implementation
• Matlab Implementations
• Animations
• Richardson's Extrapolation

Numerical Integration

• Matlab Files for Numerical Integration - use functions intf.m and intf2.m
  • Composite Trapezoidal trapezoid.m
  • Composite Simpson's simpson.m
  • Composite Midpoint midpoint.m
  • Romberg Integration romberg.m
• Maple Implementation NumInt.mws
• Monte Carlo Technique monte.m
• Gauss-Legendre Quadrature gauss.m, quadfun.m, vander2.m, LegendrePoly.m

Initial Value Problems for ODEs

• ODE course material, including using Maple, links to applets, etc
• Matlab Files - using defunc.m
  • Euler's Method euler.m
  • Modified Euler modeuler.m
  • Huen's Method huen.m
  • Runge-Kutta Order Four rk4.m
  • Adams-Bashforth Order Four AdamsBash4.m
  • Adams-Bashforth-Moulton Predictor-Corrector ABM.m
• Maple File - NumODE.mws
• Other Code - Systems discussion  included
• Stability Applet
• Stability.mws

Solving Linear Systems

• LU Decomposition in Maple
• Matlab Routines
  • Example Usage MatEx.m
  • Forward Substitution LF.m
  • Backward Substitution UB.m
  • LU Factorization lufac.m
  • LTriSol.m
• LU Factorization Examples

Matrix Methods

• Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
• Matrix Iteration Software - in German
• Iterative Methods for Sparse Systems
• Exercise
• Matlab Example of Matrix Iterations MaxIter.m
• Matrix Iteration and BVP ODEIt.m

Approximation Theory

• Linear Least Squares - Math World
• Least Squares Polynomial Fit by clicking
• Least Squares Fitting of Data from the Physical Sciences & Engineering
• Nonlinear Curve Fit Applet
• Approximation Methods PPT

Other Links

• Matlab Central
• Matlab Database
• Computational Science Modules
• Olver's Matlab Routines

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