San Antonio, Texas

Spring 2015 - Partial Differential Equations

Lecture Handouts & Slides

DateDescription
1/15 Handout:  Syllabus
1/15 Lecture:  Introduction to PDEs
1/20 Lecture:  Solving first order PDEs
1/22 Lecture:  Method of characteristics
Maple worksheet:*  Initial and characteristic curves
1/27 Lecture:  Introduction to the wave equation
Maple worksheet:*  Traveling wave solutions of the wave equation
1/29 Lecture:  Introduction to Fourier series
2/3 Lecture:  Formulas for Fourier coefficients
Maple worksheet:*  Convergence of Fourier series
2/5 Lecture:  More on Fourier series
2/17 Lecture:  Series solution of the 1-D wave equation
Maple worksheet:*  Normal modes of the 1-D wave equation
2/19 Maple worksheet:*  Series solutions of the 1-D wave equation
Lecture:  Linear PDEs and superposition
2/24 Lecture:  The 1-D heat equation, part 1
Maple worksheet:*  1-D heat examples
2/26 Lecture:  The 1-D heat equation, part 2
Maple worksheet:*  1-D heat examples
3/3 Lecture:  The 2-D wave equation: rectangular membranes
Maple worksheet:*  Rectangular 2-D wave examples
3/5 Lecture:  The 2-D heat equation:  rectangular plates
Maple worksheet:*  2-D heat example
3/17 Lecture:  The 2-D heat equation:  circular plates
3/24 Lecture:  Power series, part 1:  review of Calc. II
Maple worksheet:*  Convergence of power series
4/2 Lecture:  Power series, part 2:  solving ODEs
Maple worksheet:*  Power series ODE solutions
4/7 Lecture:  Solving ODEs via Frobenius' method
Maple worksheet:*  Plots of Frobenius' solutions
4/9 Lecture:  Bessel functions (of the first kind)
Maple worksheet:*  Normal modes of the vibrating circular membrane
4/14 Lecture:  Complete solution to the vibrating circular membrane problem
Maple worksheet:*  Examples of vibrating circular membranes
4/16 Lecture:  Sturm-Liouville Theory
4/21 Lecture:  The Fourier transform
4/23 Lecture:  Solving PDEs with the Fourier transform

*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.