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• Week-1 Introduction: Review Ordinary differential equation in more than one variables
• Week-2 Linear Partial differential equations of the first order
• Week-3 Cauchy's problem for Quasilinear first order PDEs
• Week-4 PDEs of second order in two variables with variable coefficients
• Week-5 Linear transformation from one equation to another equation
• Week-6 Normal form and Cauchy's problem for second order PDEs in two independent variables
• Week-7 Adjoint operator, self adjoint operator and operators
• Week-8 Linear PDEs in n independent variables
• Week-9 Lagrange's identity and Green's theorem for self adjoint operator
• Week-10 The Laplace equation
• Week-11 Dirichlet problem for a circle
• Week-12 Poisson's integral for a circle
• Week-13 Solution of Laplace equation in Cartesian, cylindrical and spherical coordinates
• Week-14 The wave equation in one dimension
• Week-15 The wave equation in higher dimension
• Week-16 The heat equation and Axially symmetric solutions