Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equations

Preview 37:14

Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equations

Preview 31:00

Lecture 2.6: FOPDE's - Method of characteristics for Quasilinear equations - 1

Preview 37:17

Lecture 2.8: First order Partial Differential Equations - Failure of transversality condition

Preview 37:26

Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equations

Preview 28:28

Lecture 2.10: FOPDE's- General nonlinear equations 1 - Search for a characteristic direction

Preview 37:55

Lecture 2.11:FOPDE's-General nonlinear equations 2-Characteristic direction and characteristic strip

Preview 30:22

Lecture 2.12: FOPDE's - General nonlinear equations 3 - Finding an initial strip

Preview 30:40

Lecture 2.13: FOPDE's - General nonlinear equations 4 - Local existence and uniqueness theorem

Preview 28:17

Lecture 2.14: First order Partial Differential Equations - Tutorial on General nonlinear equations

Preview 42:27

Lecture 2.15: First order Partial Differential Equations-Initial value problems for Burgers equation

Preview 33:13

Lecture 2.16: FOPDE's - Conservation laws with a view towards global solutions to Burgers equation

Preview 39:18

Lecture: 3.1: Second Order Partial Differential Equations - Special Curves associated to a PDE

Preview 42:26

Lecture: 3.2: Second Order Partial Differential Equations - Curves of discontinuity

Preview 31:16

Lecture 3.3: Second Order Partial Differential Equations - Classification

Preview 34:51

Lecture 3.4: SOPDE's - Canonical form for an equation of Hyperbolic type

Preview 21:15

Lecture 3.5: SOPDE's - Canonical form for an equation of Parabolic type

Preview 20:15

Lecture 3.6: SOPDE's - Canonical form for an equation of Elliptic type

Preview 20:15

Lecture 3.7: Second Order Partial Differential Equations - Characteristic Surfaces

Preview 40:12

Lecture 3.8: SOPDE's - Canonical forms for constant coefficient PDEs

Preview 18:36

Lecture 4.1: Wave Equation - A mathematical model for vibrating strings

Preview 31:52

Lecture 4.2: Wave Equation in one space dimension - d'Alembert formula

Preview 20:30

Lecture 4.3: Tutorial on One dimensional wave equation

Preview 54:39

Lecture 4.4: Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical means

Preview 29:20

Lecture 4.5: Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulae

Preview 21:58

Lecture 4.6: Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descent

Preview 27:31

Lecture 4.7: Nonhomogeneous Wave Equation - Duhamel principle

Preview 36:26

Lecture 4.8: Wellposedness of Cauchy problem for Wave Equation

Preview 29:25

Lecture 4.9: Wave Equation on an interval in ? - Solution to an IBVP from first principles

Preview 50:09

Lecture 4.10: Tutorial on IBVPs for wave equation

Preview 63:44

Lecture 4.11: IBVP for Wave Equation - Separation of Variables Method

Preview 37:30

Lecture 4.12: Tutorial on Separation of variables method for wave equation

Preview 49:18

Lecture 5.1: Qualitative analysis of Wave equation - Parallelogram identity

Preview 48:14

Lecture 5.2: Qualitative analysis of Wave equation - Domain of dependence, domain of influence

Preview 26:49

Lecture 5.3: Qualitative analysis of Wave equation- Causality Principle, Finite speed of propagation

Preview 32:14

Lecture 5.4: Qualitative analysis of Wave equation - Uniqueness by Energy method

Preview 33:23

Lecture 5.5: Qualitative analysis of Wave equation - Huygens Principle

Preview 27:42

Lecture 5.6: Qualitative analysis of Wave equation - Generalized solutions to Wave equation

Preview 40:26

Lecture 5.7: Qualitative analysis of Wave equation - Propagation of waves

Preview 32:11

Lecture 6.1: Laplace equation - Associated Boundary value problems

Preview 27:25

Lecture 6.2: Laplace equation - Fundamental solution

Preview 27:20

Lecture 6.3: Dirichlet BVP for Laplace equation - Green's function and Poisson's formula

Preview 31:05

Lecture 6.4: Laplace equation - Weak maximum principle and its applications

Preview 19:45

Lecture 6.5: Laplace equation - Dirichlet BVP on a disk in R2 for Laplace equations

Preview 28:36

Lecture 6:6: Tutorial 1 on Laplace equation

Preview 42:40

Lecture 6:7: Laplace equation- Mean value property

Preview 22:05

Lecture 6:8: Laplace equation- More qualitative properties

Preview 17:53

Lecture 6:9: Laplace equation- Strong Maximum Principle and Dirichlet Principle

Preview 31:25

Lecture 6:10: Tutorial 2 on Laplace equation

Preview 38:25

Lecture 7.1: Cauchy Problem for Heat Equation - 1

Preview 16:33

Lecture 7.2: Cauchy Problem for Heat Equation - 2

Preview 26:08

Lecture 7.3: IBVP for Heat equation Subtitle: Method of Separation of Variables

Preview 22:34

Lecture 7.4: Maximum principle for heat equation

Preview 26:00

Lecture 7.5: Tutorial on heat equation

Preview 16:21

Lecture 7.6: Heat equation Subheading : Infinite speed of propagation, Energy, Backward Problem

Preview 14:52