3150 Maple, Gustafson S2013

Visualizations

  1. Visualizations of waves, strings, membranes (Falstad.com)

MAPLE Sources for 3150, Asmar References

The MAPLE text sources assume familiarity with MAPLE and its HELP interface. See
Utah Maple Tutorial 2013
To use a source, mouse copy the text and paste it into a maple worksheet.

These sources are intended as study aids in understanding Asmar's problems and examples.

    Notation.
    1.0 is background for Chapter 1;
    2.7 is Chapter 2 Section 7;
    3.5-13 is Problem 13 from Chapter 3 Section 5.
There are multiple authors. Suggestions and corrections are appreciated.

    Maple Text Sources
  1. 1.0, Solve x''+4x=8 Dirac(t-2 Pi)
  2. 1.0, How to use the simplest plot interface in maple, by example
  3. 2.0-5, Triangular wave maple code example
  4. 2.1, define and plot periodic waves
  5. 2.2, Example 1, notebook from Asmar's site
  6. 2.1, Triangular wave maple code example
  7. Chapter 2, How to plot periodic waves
  8. 2.2, Gibbs phenomenon, 8 percent over-shoot
  9. 2.2-5, Asmar, problem f(x)=|x|
  10. 2.2-8, rectified cosine wave, fourier series
  11. 2.2 Asmar, 2.1 Example 3, Sawtooth function
  12. 2.3-7, f(x)=1-x Fourier sine coefficient integration
  13. 2.7 Example 1, my''+cy'+ky=F(t) with F a sawtooth wave.
  14. 3.3 notebook, Asmar's site, String with fixed ends
  15. 3.3 Example 2, Normal modes
  16. 3.4-15, D'Alembert's solution of the wave equation, f=pulses,g=0
  17. 3.4 Example 1, D'Alembert;s method
  18. 3.4 Figures, Characteristic parallelogram, interval of dependence
  19. 3.4, D'Alembert's solution wave equation, answer check for an exam problem
  20. 3.5-13, Heat equation,
  21. 3.5, Example 3, bar with one radiating end, solve tangent equation
  22. 3.5, Example 3, Robin problem, eigenvalues and integrations
  23. 3.6, Example 1, Bar with insulated ends, Neumann problem, f(x)=100
  24. 3.7-5, rectangular membrane with animation
  25. 3.7-5, rectangular membrane animation, source for making the filmstrip PDF
  26. 3.7-12, heat equation on unit square F:=4x(1-x)y(1-y)sin(m Pi x) sin(n Pi y)
  27. 3.7, Example 1, rectangular membrane, f(x,y)=x(x-1)y(y-1)
  28. 3.9-3, Poisson problem with zero conditions, f=sin(PI x)
  29. 4.2, Example 2, circular membrane, verify 1-r*r = sum A[n] J_0(alpha_n r) where A[n]=8/((alpha_n)^3*J_1(alpha_n))
  30. 4.3 Example 2, general case drumhead
  31. 4.3 Example 3, general case drumhead
  32. 4.7 and appendix A4, Find series solutions of ODE
  33. 4.7 and 4.3, plot bessel functions type J, K, Y.
  34. Chapter 7, Maple code for the Fourier transform