This course gives an introduction to analytic methods for solving partial differential equations. It also introduces learners to the famous Sturm-Lowville theory for ordinary differential equations.
At the end of this course a student must be able to, identify/classify the different types of partial differential equations, state and prove spectral properties for compact operators, compute eigen values and eigen functions for an ordinary differential equation and find the series solution to the equation, use analytic methods to solve partial differential equations.