1. Characteristics, classification of PDE, separation of variables, Fourier transform, and Laplace transform. 2. Well-posedness of the wave and the heat equations. 3. Boundary value problems for the Laplace and Poisson equations. 4. Separation of variables.

CILO-1: Apply Fourier Sine and Cosine Series, and Fourier Series in general. CILO-2: Solve classical PDEs such as elliptic, parabolic and hyperbolic. CILO-3: Identify the physical and engineering problems where such equations show up. CILO-4: Apply the method of separation of variables to solve problems in various fields, in a number of coordinate systems. CILO-5: Compute eigen-functions, and eigen-function expansion of the solutions. CILO-6: Identify square integrable functions, and analyse the completeness of eigen-function expansions.