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
