Objective: By the end of this course, I hope that

• you will understand how partial differential equation arise in some classical problems in math and physics;
• you will be familar with complex variables, complex functions and contour integrals;
• you will know how to use inttegral transforms, such as Fourier and Laplace transforms, to solve some differential equations;
• when faced with a problem involving a linear partial differential equation, you will be able to select and carry out an appropriate solution strategy;
• you will understand why linear differential equations are essentially solved once the eigenvalues and eigenvectors of the appropriate differential operators are known, and to be able to identify those operators;
• you will be comfortable using special functions such as Bessel functions.

Topics covered (tentative): Complex variables and residue calculus, Laplace transforms, Fourier transforms, Separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, Bessel functions, orthogonal polynomials, the heat equation, wave equation, and Laplace's equation.