| No | Date | Topics/Presentations |
| 1 | August 18, 2021 | Introduction: What is PDE? |
| 2 | August 23, 2021 | Industry Problems, Million Dollar Questions |
| 3 | August 25, 2021 | Classifications of First-order and Second-order PDE |
| 4 | August 27, 2021 | Classifications and Boundary Conditions |
| 5 | August 30, 2021 | Method of Characteristics-I |
| 6 | August 31, 2021 | Method of Characteristics-II |
| 7 | September 1, 2021 | Existence and Uniqueness Theorem for Quasilinear PDE |
| 8 | September 3, 2021 | Transport and Burgers Equation Derivation |
| 9 | September 6, 2021 | Rarefaction, Shock Waves and General Solution |
| 10 | September 8, 2021 | Heat/Wave/Laplace Equation - Separation of Variables |
| 11 | September 13, 2021 | Heat Equation - Derivation |
| 12 | September 15, 2021 | Wave Equation and Transport Theorem |
| 13 | September 17, 2021 | d'Alembert's Formula |
| 14 | September 22, 2021 | Euler-Poisson-Darboux Equation |
| 15 | September 24, 2021 | Kirchhoff's Formula - Wave Equation for Odd n |
| 16 | September 27, 2021 | Poisson's Formula-Wave Equation for Even n, Inhomogeneous Equation |
| 17 | September 28, 2021 | Laplace Equation - Fundamental Solution |
| 18 | September 29, 2021 | Laplace Equation - Mean Value Formula, Max-Min Principle |
| 19 | October 1, 2021 | Laplace Equation - Regularity |
| 20 | October 4, 2021 | Laplace Equation - Analyticity |
| 21 | October 1, 2021 | Basics of Distribution |
| 22 | October 18, 2021 | Laplace Equation - Green's Function |
| 23 | October 20, 2021 | Laplace Equation - Poisson's formula for Half Space and the ball |
| 24 | October 22, 2021 | Laplace Equation - Energy Methods |
| 25 | October 25, 2021 | Heat Equation - Fundamental Solution |
| 26 | October 27, 2021 | Heat Equation - In/homogeneous IVP |
| 27 | October 29, 2021 | Heat Equation - Mean Value Property |
| 28 | November 1, 2021 | Heat Equation - Maximum Principle, Regularity, Energy Methods |
| 29 | November 3, 2021 | First-Order Nonlinear PDE-Complete Integral, Envelopes, General Integral |
| 30 | November 5, 2021 | First-Order Nonlinear PDE-two variables, Complete and Singular Integral, Standard Form I |
| 31 | November 13, 2021 | First-Order Nonlinear PDE-two variables: Standard Forms and Charpit's Method |
| 32 | November 8, 2021 | First-Order Nonlinear PDE: Jacobi's Method, Classification of Second-Order Linear PDE |
| 33 | November 10, 2021 | Classification of Second-Order Linear PDE-Hyperbolic |
| 34 | November 12, 2021 | Classification of Second-Order Linear PDE-Parabolic and Elliptic |
| 35 | November 15, 2021 | Classification of Second-Order Linear PDE, Laplace Equation in Polar Coordinates and Annular Region |
| 36 | November 17, 2021 | First Order Nonlinear PDE: Characteristic ODE-1 |
| 37 | November 22, 2021 | First Order Nonlinear PDE: Characteristic ODE-2 |
| 38 | November 24, 2021 | First Order Nonlinear PDE: Characteristic ODE-3 |
| 39 | November 26, 2021 | Nonlinear PDE: Applications, Scalar Conservation Laws, Hamilton-Jacobi Equation |
| 40 | November 29, 2021 | Scalar Conservation Laws: R-H Condition |
| 41 | December 1, 2021 | Riemann Problem, Holder Space |
| 42 | December 3, 2021 | Sobolev Spaces, Milgram Theorem |
| 43 | December 3, 2021 | Milgram Theorem Proof |
| 44 | December 6, 2021 | Milgram Theorem Proof |
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 1, 2021 | September 20, 2021 |
| 2 | Assignment-2 | September 22, 2021 | October 04, 2021 |
| 3 | Assignment-3 | October 5, 2021 | October 18, 2021 |
| 4 | Assignment-4 | October 10, 2021 | November 15, 2021 |
| 5 | Assignment-5 | November 17, 2021 | December 5, 2021 |
| 6 | Assignment-6 | October 5, 2021 | December 5, 2021 |
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