Joseph M. Mahaffy SDSU
Math 531: Partial Differential Equations Spring 2019
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Lectures for Math 531

  1. Introduction (4-Panel) - Maple Commands (Maple .mw) - Maple Adoption Discount
  2. Ordinary Differential Equations (4-Panel) -
  3. Heat Equation - Derivation (4-Panel) -
  4. Heat Equation - 3D (4-Panel) -
  5. Separation of Variables (4-Panel) - heatjm.m, heat1d (PDF),
  6. Separation of Variables B (4-Panel) -
  7. Fourier Series (4-Panel) - MatLab: fourier_1.m, gibb_c.m, gibb_d.m, Maple: (PDF)
  8. String (4-Panel) -
  9. Sturm-Liouville Problems (4-Panel) -
  10. Sturm-Liouville Problems B (4-Panel) -
  11. Sturm-Liouville Problems C (4-Panel) - MatLab: fourier_rob.m, heatjm_rob.m, Maple: (PDF)
  12. Higher Dimensional PDEs (4-Panel) -
  13. Vibrating Circular Membrane (4-Panel) - MatLab: bess_jy0.m, bessel_modes.m, bessel_modesMN.m, besselzero.m, Maple: bessel.mws (PDF), membrane.mws
  14. Laplace's on Cylinder (4-Panel) -
  15. Nonhomogeneous Problems (4-Panel) -
  16. Fourier Transforms (4-Panel) -
  17. Fourier TransformsB (4-Panel) - MatLab: heatFT3D.m, heatFTarbf.m, Maple: fourier_heat.mws (PDF)
  18. Fourier TransformsC (4-Panel) - MatLab: pde_eg1.m, laplace_eg.m,
  19. Method of Characteristics (4-Panel) -

Additional Resources

There is a Lab Manual (MATLAB and Maple) version, which will continue to be updated over the semester with detailed information for using MatLab and Maple on your written assignments.



Lecture Note Supplements

Chapter 2: Programming Supplement

A class demonstration of Maple and MatLab is given for the one-dimensional heat equation. Links are provided to computer code for Maple (heat1d (PDF)) and MatLab (heatjm.m) for the Heat Equation in one-dimension.

Chapter 3: Programming Supplement

A class demonstration of a Fourier series is given. A link is provided for a MatLab M-file for this Fourier series.

Chapter 5: Programming Supplement

Finding eigenvalues for boundary conditions of the third kind . A link is provided for a Maple file to show how to numerically find eigenvalues of this transcendental equation.

Chapter 7: Programming Supplement

Visualizing vibrating rectangular membranes, we have a link for a Maple file (rect_memb.mws). Also, solutions to Bessel's differential equation are provided using Maple (bessel.mws) and a hyperlink to Maplesoft and others. Solutions to Legendre's differential equation are provided using Maple (legendre.mws).

Below are some MatLab codes and pictures from PDEs provided by Ricardo Carretero.




Heat equation in 1D: heat.m.

PDE integrator in 1D: PDE_integrator.m, wave_plotsurf.m.

Normal modes of wave equation: vibrate.m

Solutions to the linear wave equation: wave_eq.m.

D'Alambert solutions to the linear wave equation: ugauss_utzero.m.

Bessel modes: bessel_modes.m, besselzero.m.


For questions concerning the webpage contact Joseph Mahaffy.



Copyright © 2019 Joseph M. Mahaffy.