478/578 Handouts and Worksheets

• Crash course in MATLAB (Version 7) (pdf) (by Toby Driscoll)
• 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
• Additional reading
• 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)
  • anonymous_functions.m (how to use anonymous functions)
  • basics.zip (.zip file containing all of the files above)
• Chapter 1 of class notes (now complete, updated 1/31, composite Simpson fixed)
• Maple WS: Polynomial Interpolation I: Motivation
• Maple WS: Polynomial Interpolation II: Error Formula
• Maple WS: Runge Example
• Maple WS: Spline Interpolation
• Maple WS: Euler's Method and Taylor Methods
• 478578_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
• Chapter 2 of class notes (slightly updated 02/15)
• 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
• Chapter 3 of class notes (typos fixed 02/20)
• Chapter 4 of class notes
• 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)
• Chapter 5 of class notes
• Chapter 6 of class notes
• 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
• Chapter 7 of class notes (slightly updated 03/05)
• Maple worksheet for derivative estimation
• 478578_DerivativeEstimates.mws Maple worksheet that illustrates derivative estimates via polynomial interpolation
• 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
• 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
• Chapter 8 of class notes
• Chapter 9 of class notes (significantly updated 03/27)
• Matlab files for RBF Collocation
• KansaLaplace_2D.m Matlab function for solution of 2D Laplace equation with Dirichlet boundary conditions via Kansa's method
• KansaLaplaceMixedBC_2D.m Matlab function for solution of 2D Laplace equation with mixed boundary conditions via Kansa's method
• HermiteLaplace_2D.m Matlab function for solution of 2D Laplace equation with Dirichlet boundary conditions via symmetric method
• HermiteLaplaceMixedBCTref_2D.m Matlab function for solution of 2D Laplace equation with mixed boundary conditions via symmetric method
• DistanceMatrix.m Matlab function to compute a distance matrix for a given set of collocation points
• DifferenceMatrix.m Matlab function to compute a difference matrix for a given set of collocation points
• Chapter 10 of class notes
• 478578_GaussQuadrature.mws Maple worksheet that illustrates derivation of Gaussian quadrature rules
• Chapter 11 of class notes
• Matlab files for finite difference solvers
• BVPDemo.m Matlab script that calls bvpsolve.m (see Computer Assignment 4)
• bvpsolve.m Matlab function to solve BVPs by finite difference methood (added Dec.4)
• FD4Demo.m Matlab script for fourth-order finite difference differentiation
• 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
• Chapter 12 of class notes
• Chapter 13 of class notes (some typos fixed April 24)
• The FFT: an algorithm the whole family can use by Dan Rockmore, Computing in Science & Engineering 2/1 (2000), 60-64
• 478578_FFT.mws Maple worksheet that illustrates convolution smoothing of noisy data via FFT