Partial Differential Equations ZJZ8H7S9NQ

URI	`m2://res/ZJZ8H7S9NQ`
Kind	course
Creators	Sivaji Ganesh (instructor)
Date	2021-07-12
MSC	35-XX
Scope	in
Ids	course 02qyf5152:111101153

Expressions

e1: edition

Language	en
Date	2021-07-12

m1: page, IIT Bombay (record). nptel 111101153
m2: page, 2021-07-12 (record). nptel 111101153

Contents

part 1: Week 1
session 1: Lecture 1.1: Partial Differential Equations - Basic concepts and Nomenclature
session 2: Lecture 2.1: First Order Partial Differential Equations - How they arise? Cauchy Problems, IVPs, IBVPs
session 3: Lecture 2.2: First order Partial Differential Equations - Geometry of Quasilinear equations
session 4: Lecture 2.3: First order Partial Differential Equations - General Solutions to Linear and Semilinear equations
session 5: Lecture 2.4: First order Partial Differential Equations - Lagrange's method for Quasilinear equations
part 2: Week 2
session 6: Lecture 2.5: First order Partial Differential Equations - Relation between Characteristic curves and Integral surfaces for Quasilinear equations
session 7: Lecture 2.6: First order Partial Differential Equations - Method of characteristics for Quasilinear equations - 1
session 8: Lecture 2.7: First order Partial Differential Equations - Method of characteristics for Quasilinear equations - 2
session 9: Lecture 2.8: First order Partial Differential Equations - Failure of transversality condition
session 10: Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equations
part 3: Week 3
session 11: Lecture 2.10: First order Partial Differential Equations - General nonlinear equations 1 - Search for a characteristic direction
session 12: Lecture 2.11: First order Partial Differential Equations - General nonlinear equations 2 - Characteristic direction and characteristic strip
session 13: Lecture 2.12: First order Partial Differential Equations - General nonlinear equations 3 - Finding an initial strip
session 14: Lecture 2.13: First order Partial Differential Equations - General nonlinear equations 4 - Local existence and uniqueness theorem
session 15: Lecture 2.14: First order Partial Differential Equations - Tutorial on General nonlinear equations
part 4: Week 4
session 16: Lecture 2.15: First order Partial Differential Equations - Initial value problems for Burgers equation
session 17: Lecture 2.16: First order Partial Differential Equations - Conservation laws with a view towards global solutions to Burgers equation
session 18: Lecture 3.1: Second Order Partial Differential Equations - Special Curves associated to a PDE
session 19: Lecture 3.2: Second Order Partial Differential Equations - Curves of discontinuity
part 5: Week 5
session 20: Lecture 3.3: Second Order Partial Differential Equations - Classification
session 21: Lecture 3.4: Second Order Partial Differential Equations - Canonical form for an equation of Hyperbolic type
session 22: Lecture 3.5: Second Order Partial Differential Equations -Canonical form for an equation of Parabolic type
session 23: Lecture 3.6: Second Order Partial Differential Equations - Canonical form for an equation of Elliptic type
session 24: Lecture 3.7: Second Order Partial Differential Equations - Characteristic Surfaces
session 25: Lecture 3.8: Second Order Partial Differential Equations - Canonical forms for constant coefficient PDEs
part 6: Week 6
session 26: Lecture 4.1: Wave Equation - A mathematical model for vibrating strings
session 27: Lecture 4.2: Wave Equation in one space dimension - d'Alembert formula
session 28: Lecture 4.3: Tutorial on One dimensional wave equation
session 29: Lecture 4.4: Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical means
session 30: Lecture 4.5: Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulae
session 31: Lecture 4.6: Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descent
part 7: Week 7
session 32: Lecture 4.7: Nonhomogeneous Wave Equation - Duhamel principle
session 33: Lecture 4.8: Wellposedness of Cauchy problem for Wave Equation
session 34: Lecture 4.9: Wave Equation on an interval in ℝ - Solution to an IBVP from first principles
session 35: Lecture 4.10: Tutorial on IBVPs for wave equation
part 8: Week 8
session 36: Lecture 4.11: IBVP for Wave Equation - Separation of Variables Method
session 37: Lecture 4.12: Tutorial on Separation of variables method for wave equation
session 38: Lecture 5.1: Qualitative analysis of Wave equation - Parallelogram identity
session 39: Lecture 5.2: Qualitative analysis of Wave equation - Domain of dependence, domain of influence
part 9: Week 9
session 40: Lecture 5.3: Qualitative analysis of Wave equation - Causality Principle, Finite speed of propagation
session 41: Lecture 5.4: Qualitative analysis of Wave equation - Uniqueness by Energy method
session 42: Lecture 5.5: Qualitative analysis of Wave equation - Huygens Principle
session 43: Lecture 5.6: Qualitative analysis of Wave equation - Generalized solutions to Wave equation
session 44: Lecture 5.7: Qualitative analysis of Wave equation - Propagation of waves
part 10: Week 10
session 45: Lecture 6:1: Laplace equation - Associated Boundary value problems
session 46: Lecture 6:2: Laplace equation - Fundamental solution
session 47: Lecture 6:3: Dirichlet BVP for Laplace equation - Green's function and Poisson's formula
session 48: Lecture 6:4: Laplace equation -Weak maximum principle and its applications
session 49: Lecture 6:5: Laplace equation - Dirichlet BVP on a disk in ℝ2 for Laplace equations
session 50: Lecture 6:6: Tutorial 1 on Laplace equation
part 11: Week 11
session 51: Lecture 6:7: Laplace equation - Mean value property
session 52: Lecture 6:8: Laplace equation - More qualitative properties
session 53: Lecture 6:9: Laplace equation - Strong Maximum Principle and Dirichlet Principle
session 54: Lecture 6:10: Tutorial 2 on Laplace equation
part 12: Week 12
session 55: Lecture 7.1: Cauchy Problem for Heat Equation - 1
session 56: Lecture 7.2: Cauchy Problem for Heat Equation - 2
session 57: Lecture 7.3: IBVP for Heat equation Subtitle: Method of Separation of Variables
session 58: Lecture 7.4: Maximum principle for heat equation
session 59: Lecture 7.5: Tutorial on heat equation
session 60: Lecture 7.6: Heat equation Subheading : Infinite speed of propagation, Energy, Backward Problem

Catalogue records

nptel: 111101153 (manifestation)
nptel_video: 111101153 (manifestation)