472 Handouts and Worksheets

• A Practical Introduction to Matlab (Version 5) (html version) (by Mark Gockenbach) or Postscript version
• For more introductory material and tutorials see the main course page
• Introductory Matlab scripts
  • basic_definitions.m (script that calls all other files. Note, however, that each file below can also be executed separately.)
  • matrix_vector.m (definition of matrices and vectors)
  • arithmetic.m (simple arithmetic with matrices and vectors)
  • lin_sys.m (solving linear systems)
  • submatrices.m (definition of submatrices)
  • statistics.m (timing in Matlab)
  • loops.m (for-loops, and why to avoid them)
  • plotting.m (simple plotting)
  • user_defined_functions.m (how to use user-defined functions)
  • circle.m (a user-defined function)
  • inline_functions.m (how to use inline functions)
  • basics.zip (.zip file containing all of the files above)
• Polynomial Interpolation
  • PolynomialInterpolationDemo.m (script that calls PolynomialInterpolation.m)
  • PolynomialInterpolation.m (function for polynomial interpolation)
• 472_Euler_Taylor.mws (Maple worksheet about Euler's method and Taylor seris methods)
• 472_ODESystems.mws (Maple worksheet about systems of ODEs)
• Euler's method
  • Euler.m Matlab function for Euler's method
  • EulerDemo.m Matlab script that calls Euler.m
• Trapezoidal Rule
  • Trapezoid.m Matlab function for trapezoidal rule
  • TrapezoidDemo.m Matlab script that calls Trapezoid.m
• Convergence for non-Lipschitz functions
  • EulerFailDemo.m Matlab script for Euler's method
  • TrapezoidFailDemo.m Matlab script for trapezoidal rule
• Convergence for Adams-Bashforth method
  • ABDemo.m Matlab script for comparison of Euler's and AB2 method
  • AB2.m Matlab script for second-order Adams-Bashforth method
• Explicit vs. implicit multistep methods
  • StiffDemo.m Matlab script for comparison of AB2 and BDF2 methods
  • AB2System.m Matlab script for second-order Adams-Bashforth method for systems
  • BDF2System.m Matlab script for second-order BDF method for systems
• Stiff Equations
  • StiffDemo2.m Matlab script for demonstration of a stiff problem
  • StiffDemo2.mws Maple worksheet that computes exact solution for the stiff problem in StiffDemo2.m
  • VanderPolDemo.m Matlab script for Van der Pol equations (another stiff problem)
• Matlab scripts for Newton's method for nonlinear systems
• Matlab m-file for Newton's method for nonlinear systems
• Matlab script file that calls newtonmv.m
• Matlab m-file defining the functions used in run_newtonmv.m
• Matlab m-file defining the Jacobian used in run_newtonmv.m
• .zip file containing the Matlab files above
• Matlab scipts for Longjump example
• Longjump.m Matlab script that acts as driver
• LongjumpEvent.m Matlab function that provides event for stopping the ODE solver
• Jump.m Matlab script that defines ODE system
• Maple worksheet for derivative estimation
• 472_DerivativeEstimates.mws Maple worksheet that illustrates derivative estimates via polynomial interpolation
• Matlab files for tridiagonal system solver
• tridiag.m Matlab function for solution of tridiagonal linear system with simple Gaussian elimination
• TridiagDemo.m Matlab driver script for function tridiag.m
• Matlab files for spectral methods
• PSBVP.m Matlab function that solves 2-pt BVP with pseudospectral method (modified Dec.3)
• cheb.m Matlab function that provides Chebyshev differentiation matrix
  
• PSBVPDemo.m Matlab script that calls both bvpsolve.m (see Computer Assignment 4) and PSBVP.m (modified Dec.3)
• PSDemo.m Matlab script that illustrates convergence of periodic spectral method
• BandLimitedDemo.m Matlab script that illustrates band-limited interpolation
• SpectralDiffDemo.m Matlab script that illustrates spectral differentiation with differentiation matrices
• SpectralDiffFFTDemo.m Matlab script that illustrates spectral differentiation with FFT
• ChebyshevAccuracyDemo.m Matlab script that illustrates accuracy of spectral differentiation on bounded intervals (non-periodic case)
• NonlinearPSBVPDemo.m Matlab script that illustrates use of differentiation matrices for nonlinear BVPs
• PSBVPNonHomoBCDemo.m Matlab script that illustrates use of differentiation matrices for linear BVPs with nonhomogeneous BCs
• PSBVPMixedBCDemo.m Matlab script that illustrates use of differentiation matrices for linear BVPs with mixed BCs
• 472Notes.pdf Notes for Chapters 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 (updated 12/03/05)