Lecture 1 - Partial Differential Equations - Basic concepts and Nomenclature

Lecture 2 - First Order Partial Differential Equations- How they arise? Cauchy Problems, IVPs, IBVPs

Lecture 3 - First order Partial Differential Equations - Geometry of Quasilinear equations

Lecture 4 - FOPDE's - General Solutions to Linear and Semilinear equations

Lecture 5 - First order Partial Differential Equations- Lagrange's method for Quasilinear equations

Lecture 6 - Relation between Characteristic curves and Integral surfaces for Quasilinear equations

Lecture 7 - Relation between Characteristic curves and Integral surfaces for Quasilinear equations

Lecture 8 - FOPDE's - Method of characteristics for Quasilinear equations - 1

Lecture 9 - First order Partial Differential Equations - Failure of transversality condition

Lecture 10 - First order Partial Differential Equations - Tutorial of Quasilinear equations

Lecture 11 - FOPDE's - General nonlinear equations 1 - Search for a characteristic direction

Lecture 12 - FOPDE's - General nonlinear equations 2 - Characteristic direction and characteristic strip

Lecture 13 - FOPDE's - General nonlinear equations 3 - Finding an initial strip

Lecture 14 - FOPDE's - General nonlinear equations 4 - Local existence and uniqueness theorem

Lecture 15 - First order Partial Differential Equations - Tutorial on General nonlinear equations

Lecture 16 - First order Partial Differential Equations - Initial value problems for Burgers equation

Lecture 17 - FOPDE's - Conservation laws with a view towards global solutions to Burgers equation

Lecture 18 - Second Order Partial Differential Equations - Special Curves associated to a PDE

Lecture 19 - Second Order Partial Differential Equations - Curves of discontinuity

Lecture 20 - Second Order Partial Differential Equations - Classification

Lecture 21 - SOPDE's - Canonical form for an equation of Hyperbolic type

Lecture 22 - SOPDE's - Canonical form for an equation of Parabolic type

Lecture 23 - SOPDE's - Canonical form for an equation of Elliptic type

Lecture 24 - Second Order Partial Differential Equations - Characteristic Surfaces

Lecture 25 - SOPDE's - Canonical forms for constant coefficient PDEs

Lecture 26 - Wave Equation - A mathematical model for vibrating strings

Lecture 27 - Wave Equation in one space dimension - d'Alembert formula

Lecture 28 - Tutorial on One dimensional wave equation

Lecture 29 - Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical means

Lecture 30 - Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulae

Lecture 31 - Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descent

Lecture 32 - Nonhomogeneous Wave Equation - Duhamel principle

Lecture 33 - Wellposedness of Cauchy problem for Wave Equation

Lecture 34 - Wave Equation on an interval in? - Solution to an IBVP from first principles

Lecture 35 - Tutorial on IBVPs for wave equation

Lecture 36 - IBVP for Wave Equation - Separation of Variables Method

Lecture 37 - Tutorial on Separation of variables method for wave equation

Lecture 38 - Qualitative analysis of Wave equation - Parallelogram identity

Lecture 39 - Qualitative analysis of Wave equation - Domain of dependence, domain of influence

Lecture 40 - Qualitative analysis of Wave equation - Causality Principle, Finite speed of propagation

Lecture 41 - Qualitative analysis of Wave equation - Uniqueness by Energy method

Lecture 42 - Qualitative analysis of Wave equation - Huygens Principle

Lecture 43 - Qualitative analysis of Wave equation - Generalized solutions to Wave equation

Lecture 44 - Qualitative analysis of Wave equation - Propagation of waves

Lecture 45 - Laplace equation - Associated Boundary value problems

Lecture 46 - Laplace equation - Fundamental solution

Lecture 47 - Dirichlet BVP for Laplace equation - Green's function and Poisson's formula

Lecture 48 - Laplace equation - Weak maximum principle and its applications

Lecture 49 - Laplace equation - Dirichlet BVP on a disk in R2 for Laplace equations

Lecture 50 - Tutorial 1 on Laplace equation

Lecture 51 - Laplace equation - Mean value property

Lecture 52 - Laplace equation - More qualitative properties

Lecture 53 - Laplace equation - Strong Maximum Principle and Dirichlet Principle

Lecture 54 - Tutorial 2 on Laplace equation

Lecture 55 - Cauchy Problem for Heat Equation - 1

Lecture 56 - Cauchy Problem for Heat Equation - 2

Lecture 57 - IBVP for Heat equation Subtitle: Method of Separation of Variables

Lecture 58 - Maximum principle for heat equation

Lecture 59 - Tutorial on heat equation

Lecture 60 - Heat equation Subheading : Infinite speed of propagation, Energy, Backward Problem