Software Listing of Author : "Howard Wilson"

Programs from the third edition of 'Advanced Mathematics and Mechanics Applications Using MATLAB', by Howard Wilson, Louis Turcotte and David Halpern, CRC Press, 2003, ISBN 1-58488-262-X. Contains about 12,000 lines of MATLAB programs and utilities emphasizing problems in engineering, applied math, and physics.

  • Platform: Matlab, Scripts

This workspace employs interactive graphics and Muller's method to compute function roots in a rectangular region of the complex plane. Function interact employs surface and contour plots of -log(abs(function(z))) to locate function roots which are read interactively with the graphics cursor and then corrected by function muller which computes one or several roots at a time. Ten examples involving various special functions are presented. The principal references for this work are: 'Elementary Numerical Analysis' by S.D. Conte and Carl de Boor and 'Handbook of Mathematical Functions' by Milton Abramowitz and Irene A. Stegun The following functions and files are included: interact.m - interactive driver program using graphics and function muller to compute roots in a user chosen region of the complex plane muller.m - a...

  • Platform: Matlab, Scripts

Programs and utility functions using the Symbolic Math Toolbox are provided to analyze vectors and tensors in general curvilinear coordinates. The programs perform the following functions: 1) runcoord plots intersecting coordinate surfaces for typical coordinate systems 2) runmetric computes and prints metric tensor properties a general curvilinear coordinate system 3) rundivcrl verifies agreement of numerical values of divergence and curl of an arbitrary vector computed in both cartesian and curvilinear coordinates 4) runconic plots surfaces illustrating how intersections of a cone and a plane produce conic section curves. 5) Testmetric computes properties for nine different coordinate systems and places the output in runmetric.tst. The symbolic equations from some of the examples are fairly complicated. The programs...

  • Platform: Matlab, Scripts

Program FFT2SURF plots double Fourier series representations for several different surfaces. The figures show effects of the number of series terms and use of Lanczos sigma factors to smooth Gibbs oscillations. The Fourier series of a doubly periodic function with periods px and py has the approximate form: f(x,y) = sum( exp(2i*pi/px*k*x)*c(k,m)*exp(2i*pi/py*m*y),... k=-n:n, m=-n:n) If the function has discontinuities, a better approximation can sometimes be produced by using a smoothed function fa(x,y) obtained by local averaging of f(x,y) as follows: fa(x,y) = integral(f(x+u,y+v)*du*dv, -s<u<+s, -s<v<+s )/(4*s^2) where s is a small fraction of min(px,py). Wherever f(x,y) is smooth, f and fa will agree closely, but sharp edges of f(x,y) get rounded off in the averaged function fa(x,y). The Fourier...

  • Platform: Matlab, Scripts

The output figures will show effects of the number of series terms and use of the Lanczos sigma factors to smooth the Gibbs oscillations.

  • Platform: Matlab, Scripts

The animated response of several classical system models is presented. Examples include a) large amplitude pendulum motion b) falling elastic cable c) forced response of a spring-mass-damper system d) vibrating string either released with initial deflection, or shaken at one end, or subjected to a moving load e) beam released with initial deflection f) vibration modes for an elliptic membrane and for a pin-connected truss g) forced wave propagation in rectangular or circular membranes. The analyses employ Runge-Kutta integration, Fourier expansions, and algebraic eigenvalue calculations presented in the book Advanced Mathematics and Mechanics Applications Using MATLAB, 3rd Ed., by Howard Wilson, Louis Turcotte, and David Halpern, CRC Press, 2003. To see how to run the program, use the command 'type contents' in the workspace...

  • Platform: Matlab, Scripts

Dynamical analyses in engineering often require inertial properties of complex shapes such as polyhedra. The volume, the first moment of volume and the second moment of volume of a general solid can be computed by V = Integral( dVol ), VR = Integral( R*dVol ), VRR = Integral( R*R'*dVol ). Also of interest are the centroidal radius RC = VR/V and the inertia tensor I = eye(3,3)*trace( VRR )-VRR. The Gauss divergence theorem for a tensor function F states that Integral( div(F)*dVol ) = SurfIntegral( Dot(N,F)*dSurf ) where R = [x; y; z] is the cartesian radius vector and N is the outward directed unit surface normal. This leads to [V, VR, VRR] = SurfIntegral( [ 1/3, R/4, R*R'/5 ]*Dot(N,R)*dSurf ). The surface parts of a polyhedron have constant surface normals and the integrals over planar parts can be converted to...

  • Platform: Matlab, Scripts

The modal functions of an elliptic membrane with fixed edges are expressed as products of angular and radial Mathieu functions with the natural frequencies being found in terms of the zeros of the radial functions. Routines to compute functions ce,se, Mc1 and Ms1 are provided. Mode shapes are presented using either animated surface plots or contour plots. The main driver program and associated functions are explained by using the command 'type contents' in the related workspace

  • Platform: Matlab, Scripts
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