Heat Equation, Sturm-Liouville, and
Eigenfunction Expansions
Click here
Bessel Functions: Heat and Wave Equation
Click here
Laplace Transform Techniques
Click
here
Laplace and Poisson's Equation: Qualitative
Properties Click here
Laplacian in a Sphere: Legendre Polynomials
Click here
Appendix: Generating function for Legendre Click here
Appendix: Spherical Harmonics Click here
Wave Equation on Infinite Domains:
D'Alembert's representation
Click here
Fourier Integral Transforms:
Fourier Transforms Click here
Method of Characteristics:
Click here: Example on Finding
General Solution Click here
Notes on Quasiliner PDE, Shocks, Fans, and
Traffic Flow Click here
New notes on shock formation,expansion fans. Worked
problems Click here
Notes on the Eikonal Equation
Click here: Notes on Finding the
Envelope Click here