San Antonio, Texas

Spring 2012 - Partial Differential Equations

Lecture Handouts & Slides

DateDescription
1/12 Handout:  Syllabus
1/12 Maple worksheet:*  The transport equation
1/17 Maple worksheet:*  Method of characteristic curves
1/19 Maple worksheet:*  Traveling wave solutions to the wave equation
Maple worksheet:*  d'Alembert's solution
1/24 Maple worksheet:*  Normal modes of the vibrating string
1/26 Maple worksheet:*  Piecewise smooth periodic functions
1/31 Maple worksheet:*  Partial sums of Fourier series
2/16 Maple worksheet:*  Dominant mode of a forced oscillation
2/21 Maple worksheet:*  Fourier series solutions to the wave equation
2/23 Maple worksheet:*  Solutions to the heat equation
2/28 Lecture:  Neumann and Robin boundary conditions
Maple worksheet:*  Solution to the heat equation with Neumann boundary conditions
3/1 Maple worksheet:*  Solution to the heat equation with Robin boundary conditions
Lecture:  The two dimensional wave equation
Maple worksheet:*  Normal modes of a rectangular membrane
3/6 Maple worksheet:*  Sample solution to the two dimensional wave equation
Lecture:  The two dimensional heat equation
Maple worksheet:*  Sample solution to the two dimensional heat equation
3/27 Maple worksheet:*  The Dirichlet problem on a rectangle: single inhomogenous boundary condition
Maple worksheet:*  The Dirichlet problem on a rectangle: multiple inhomogenous boundary conditions
Lecture:  The Dirichlet problem on a rectangle
Lecture:  The Laplacian in polar coordinates
3/29 Lecture:  The circular membrane problem
Maple worksheet:*  Bessel functions
Maple worksheet:*  Normal modes of the vibrating circular membrane
4/3 Lecture:  More on the circular membrane problem
4/5 Lecture:  Examples of the circular membrane problem
Maple worksheet:*  A radially symmetric vibrating circular membrane
Maple worksheet:*  A non-symmetric vibrating circular membrane
Maple worksheet:*  A "complicated" vibrating circular membrane
4/10 Lecture:  Intro to Sturm-Liouville theory
4/19 Lecture:  More on Sturm-Liouville theory

*To use any of the Maple worksheets above, first download it (right click and "Save Link As...") and then open it, using a computer on which Maple has already been installed.  Maple is widely available across the campus, but if you'd like to have it installed on a particular University-owned machine, let me know and I'll see what can be done.

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Questions and comments concerning this page are to be addressed to rdaileda at trinity dot edu.