Emphasis in this course is on “computational” techniques in the sense that we will solve lots of problems (not in the sense of programming). Theory will be presented when it is especially beautiful or enlightening, and has a useful purpose. For example, Sturm-Liouville Theory, Potential Theory. Students may be asked to using plotting packages (Matlab, Python) to plot solutions to problems posed in class, but numerical methods will not be discussed in this course, except in passing.

Topics

• Power series methods for ODEs. (Bessel equation, Legendre equation)
• Sturm-Liouville theory
• Transforms (Laplace, Fourier)
• Green’s functions solutions to PDEs
• Similarity solutions
• Potential Theory, integral equations
• Calculus of Variations (Euler-Lagrange Equations)