Mathematical Physics I
 Introduction
 Finitedimensional vector spaces

Vector spaces and linear operators

Eigenvalues and eigenvectors

Diagonalization and quadratic forms
 Ordinary differential equations
 Linear equations with constant coefficients
 General firstorder and secondorder equations
 Power series solutions about a regular singular point
 SturmLiouville theory
 Orthogonal polynomials
 SturmLiouville eigenvalue problems
 Fourier series expansions
 Partial differential equations
 Wave and heat equations: one dimension
 Laplace equation: two dimensions
 Schrodinger equation: three dimensions
 Characteristics of secondorder PDEs
 Integral transforms
 Fourier transform and applications
 Laplace transform and applications