Learn · Partial Differential Equations - IITB
Lecture 17 of 60Week 4
Lecture 2.16: First order Partial Differential Equations - Conservation laws with a view towards global solutions to Burgers equation
Prof. Sivaji Ganesh · IIT Bombay
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All the lectures
- Lecture 1.1: Partial Differential Equations - Basic concepts and Nomenclature
- Lecture 2.1: First Order Partial Differential Equations - How they arise? Cauchy Problems, IVPs, IBVPs
- Lecture 2.2: First order Partial Differential Equations - Geometry of Quasilinear equations
- Lecture 2.3: First order Partial Differential Equations - General Solutions to Linear and Semilinear equations
- Lecture 2.4: First order Partial Differential Equations - Lagrange's method for Quasilinear equations
- Lecture 2.5: First order Partial Differential Equations - Relation between Characteristic curves and Integral surfaces for Quasilinear equations
- Lecture 2.6: First order Partial Differential Equations - Method of characteristics for Quasilinear equations - 1
- Lecture 2.7: First order Partial Differential Equations - Method of characteristics for Quasilinear equations - 2
- Lecture 2.8: First order Partial Differential Equations - Failure of transversality condition
- Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equations
- Lecture 2.10: First order Partial Differential Equations - General nonlinear equations 1 - Search for a characteristic direction
- Lecture 2.11: First order Partial Differential Equations - General nonlinear equations 2 - Characteristic direction and characteristic strip
- Lecture 2.12: First order Partial Differential Equations - General nonlinear equations 3 - Finding an initial strip
- Lecture 2.13: First order Partial Differential Equations - General nonlinear equations 4 - Local existence and uniqueness theorem
- Lecture 2.14: First order Partial Differential Equations - Tutorial on General nonlinear equations
- Lecture 2.15: First order Partial Differential Equations - Initial value problems for Burgers equation
- Lecture 2.16: First order Partial Differential Equations - Conservation laws with a view towards global solutions to Burgers equation
- Lecture 3.1: Second Order Partial Differential Equations - Special Curves associated to a PDE
- Lecture 3.2: Second Order Partial Differential Equations - Curves of discontinuity
- Lecture 3.3: Second Order Partial Differential Equations - Classification
- Lecture 3.4: Second Order Partial Differential Equations - Canonical form for an equation of Hyperbolic type
- Lecture 3.5: Second Order Partial Differential Equations -Canonical form for an equation of Parabolic type
- Lecture 3.6: Second Order Partial Differential Equations - Canonical form for an equation of Elliptic type
- Lecture 3.7: Second Order Partial Differential Equations - Characteristic Surfaces
- Lecture 3.8: Second Order Partial Differential Equations - Canonical forms for constant coefficient PDEs
- Lecture 4.1: Wave Equation - A mathematical model for vibrating strings
- Lecture 4.2: Wave Equation in one space dimension - d'Alembert formula
- Lecture 4.3: Tutorial on One dimensional wave equation
- Lecture 4.4: Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical means
- Lecture 4.5: Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulae
- Lecture 4.6: Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descent
- Lecture 4.7: Nonhomogeneous Wave Equation - Duhamel principle
- Lecture 4.8: Wellposedness of Cauchy problem for Wave Equation
- Lecture 4.9: Wave Equation on an interval in ℝ - Solution to an IBVP from first principles
- Lecture 4.10: Tutorial on IBVPs for wave equation
- Lecture 4.11: IBVP for Wave Equation - Separation of Variables Method
- Lecture 4.12: Tutorial on Separation of variables method for wave equation
- Lecture 5.1: Qualitative analysis of Wave equation - Parallelogram identity
- Lecture 5.2: Qualitative analysis of Wave equation - Domain of dependence, domain of influence
- Lecture 5.3: Qualitative analysis of Wave equation - Causality Principle, Finite speed of propagation
- Lecture 5.4: Qualitative analysis of Wave equation - Uniqueness by Energy method
- Lecture 5.5: Qualitative analysis of Wave equation - Huygens Principle
- Lecture 5.6: Qualitative analysis of Wave equation - Generalized solutions to Wave equation
- Lecture 5.7: Qualitative analysis of Wave equation - Propagation of waves
- Lecture 6:1: Laplace equation - Associated Boundary value problems
- Lecture 6:2: Laplace equation - Fundamental solution
- Lecture 6:3: Dirichlet BVP for Laplace equation - Green's function and Poisson's formula
- Lecture 6:4: Laplace equation -Weak maximum principle and its applications
- Lecture 6:5: Laplace equation - Dirichlet BVP on a disk in ℝ2 for Laplace equations
- Lecture 6:6: Tutorial 1 on Laplace equation
- Lecture 6:7: Laplace equation - Mean value property
- Lecture 6:8: Laplace equation - More qualitative properties
- Lecture 6:9: Laplace equation - Strong Maximum Principle and Dirichlet Principle
- Lecture 6:10: Tutorial 2 on Laplace equation
- Lecture 7.1: Cauchy Problem for Heat Equation - 1
- Lecture 7.2: Cauchy Problem for Heat Equation - 2
- Lecture 7.3: IBVP for Heat equation Subtitle: Method of Separation of Variables
- Lecture 7.4: Maximum principle for heat equation
- Lecture 7.5: Tutorial on heat equation
- Lecture 7.6: Heat equation Subheading : Infinite speed of propagation, Energy, Backward Problem