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 plot details using square wave extension
  13. 2.3-7, f(x)=1-x plot details using a recursively defined extension
  14. 2.3-7, f(x)=1-x Fourier sine coefficient integration
  15. 2.7 Example 1, my''+cy'+ky=F(t) with F a sawtooth wave.
  16. 3.3 notebook, Asmar's site, String with fixed ends
  17. 3.3 Example 2, Normal modes
  18. Problem 3.3-9b, 4-frame filmstrip
  19. 3.4-15, D'Alembert's solution of the wave equation, f=pulses,g=0
  20. 3.4 Example 1, D'Alembert;s method
  21. 3.4 Figures, Characteristic parallelogram, interval of dependence
  22. 3.4, D'Alembert's solution wave equation, answer check for an exam problem
  23. 3.5-13, Heat equation,
  24. 3.5, Example 3, bar with one radiating end, solve tangent equation
  25. 3.5, Example 3, Robin problem, eigenvalues and integrations
  26. 3.6, Example 1, Bar with insulated ends, Neumann problem, f(x)=100
  27. 3.7-5, rectangular membrane with animation
  28. 3.7-5, rectangular membrane animation, source for making the filmstrip PDF
  29. 3.7-12, heat equation on unit square F:=4x(1-x)y(1-y)sin(m Pi x) sin(n Pi y)
  30. 3.7, Example 1, rectangular membrane, f(x,y)=x(x-1)y(y-1)
  31. 3.9-3, Poisson problem with zero conditions, f=sin(PI x)
  32. Problem 4.0-4, Frobenius method maple assist, x^2y''-x(2+x)+2xy=0
  33. 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))
  34. 4.3 Example 2, general case drumhead
  35. Problem 4.3-3, general case drumhead, f=(a^2-r^2)r sin(theta), g=1
  36. 4.3 Example 3, general case drumhead
  37. 4.4 Problems 21-22-23, implicit plot of circles for isotherms
  38. 4.7 and appendix A4, Find series solutions of ODE
  39. 4.7 and 4.3, plot bessel functions type J, K, Y.
  40. Chapter 7, Maple code for the Fourier transform
  41. Chapter 7, 7.1, Gibbs overshoot for the unit pulse on |x|<1
  42. Chapter 7, Example 2, impulse response f(t)=exp(-t)Heaviside(t).
    Find FT[f] and plot magnitude and phase spectra.
  43. Chapter 7, impulse response f(t)=exp(-t/5)Heaviside(t).
    Find FT[f] and plot magnitude and phase spectra. All maple.