Partial Differential Equations

No Date Topics/Presentations
1 September 1, 2020 Introduction: What is PDE?
2 September 3, 2020 Industry Problems, Million Dollar Questions
3 September 4, 2020 Classifications of First-order and Second-order PDE
4 September 8, 2020 Classifications and Boundary Conditions
5 September 10, 2020 Method of Characteristics-I
6 September 11, 2020 Method of Characteristics-II
7 September 15, 2020 Existence and Uniqueness Theorem for Quasilinear PDE
8 September 17, 2020 Transport and Burgers Equation Derivation
9 September 18, 2020 Rarefaction, Shock Waves and General Solution
10 September 22, 2020 Heat/Wave/Laplace Equation - Separation of Variables
11 September 24, 2020 Heat Equation - Derivation
12 September 25, 2020 Wave Equation and Transport Theorem
13 September 29, 2020 d'Alembert's Formula
14 October 1, 2020 Euler-Poisson-Darboux Equation
15 October 6, 2020 Kirchhoff's Formula - Wave Equation for Odd n
16 October 8, 2020 Poisson's Formula-Wave Equation for Even n, Inhomogeneous Equation
17 October 9, 2020 Laplace Equation - Fundamental Solution
18 October 13, 2020 Laplace Equation - Mean Value Formula, Max-Min Principle
19 October 15, 2020 Laplace Equation - Regularity
20 October 16, 2020 Laplace Equation - Analyticity
21 October 20, 2020 Basics of Distribution
22 October 27, 2020 Laplace Equation - Green's Function
23 October 29, 2020 Laplace Equation - Poisson's formula for Half Space and the ball
24 November 3, 2020 Laplace Equation - Energy Methods
25 November 3, 2020 Heat Equation - Fundamental Solution
26 November 5, 2020 Heat Equation - In/homogeneous IVP
27 November 5, 2020 Heat Equation - Mean Value Property
28 November 6, 2020 Heat Equation - Maximum Principle, Regularity, Energy Methods
29 November 10, 2020 First-Order Nonlinear PDE-Complete Integral, Envelopes, General Integral
30 November 12, 2020 First-Order Nonlinear PDE-two variables, Complete and Singular Integral, Standard Form I
31 November 13, 2020 First-Order Nonlinear PDE-two variables: Standard Forms and Charpit's Method
32 November 17, 2020 First-Order Nonlinear PDE: Jacobi's Method, Classification of Second-Order Linear PDE
33 November 19, 2020 Classification of Second-Order Linear PDE-Hyperbolic
34 November 19, 2020 Classification of Second-Order Linear PDE-Parabolic and Elliptic
35 November 20, 2020 Classification of Second-Order Linear PDE, Laplace Equation in Polar Coordinates and Annular Region
36 November 24, 2020 First Order Nonlinear PDE: Characteristic ODE-1
37 November 27, 2020 First Order Nonlinear PDE: Characteristic ODE-2
38 December 1, 2020 First Order Nonlinear PDE: Characteristic ODE-3
39 December 3, 2020 Nonlinear PDE: Applications, Scalar Conservation Laws, Hamilton-Jacobi Equation
40 December 4, 2020 Scalar Conservation Laws: R-H Condition
41 December 8, 2020 Riemann Problem, Holder Space
42 December 10, 2020 Sobolev Spaces, Milgram Theorem
43 December 11, 2020 Milgram Theorem Proof
44 December 15, 2020 Milgram Theorem Proof

Mid Term Solutions

For Animations of PDE related works, refer this page

Heat Equation
Wave Equation
Poisson Equation
No Assignments Issue Date Due Date
1 Assignment-1 September 4, 2020 September 27, 2020
2 Assignment-2 October 11, 2020 October 31, 2020
3 Assignment-3 October 11, 2020 October 31, 2020
4 Assignment-4 November 1, 2020 November 30, 2020
5 Assignment-5 November 1, 2020 December 5, 2020
6 Assignment-6 November 1, 2020 December 10, 2020

Partial Differential Equations in the 20th Century
History of PDE
Seventy Five Unsolved Problems in Analysis and PDE
Millennium Problems - Navier-Stokes Equation
Volume of n-balls
Shock Waves in Plane
Supersonic Bullet
Space Shuttle Columbia Kapana Chawla Death
Shock wave Interaction
Shock wave in Traffic Flow Model
Reynolds Transport Theorem Pictorial Proof
Coarea Formula
Laplace Equation in Spherical Coordinates