The mission of this course is to develop a rigorous theoretical foundation in partial differential equations. Emphasizing classification, existence and uniqueness of solutions, and fundamental solution techniques, the course aims to cultivate a deep understanding of the mathematical structures underlying PDEs.
This course provides a rigorous introduction to the theory of partial differential equations, focusing on classical solution methods, analytical techniques, and the mathematical foundations underlying elliptic, parabolic, and hyperbolic equations. Students will explore canonical PDEs, boundary value problems, and fundamental principles such as existence, uniqueness, and stability of solutio
Lectures
Tests
End Semester
Major Topics
| # | Topic | |
|---|---|---|
| 1 | Monday | 8:00 - 8:50 |
| 2 | Wednesday | 8:00 - 8:50 |
| 3 | Friday | 8:00 - 8:50 |
| # | Assessment | Marks | Topics |
|---|---|---|---|
| 1 | Test 1 | 20 | Up to Topics Covered on 5th September 2025 |
| 2 | Test 2 | 20 | Up to Topics Covered on 8th October 2025 |
| 3 | End Semester | 60 | End Semester |
| # | Topic | |
|---|---|---|
| 1 | Introduction, History, Prerequisites | Lecture-1 |
| 2 | Preliminaries, What is PDE? | Lecture-2 |
| 3 | Applications | Lecture-3 |
| 4 | Classifications-I | Lecture-4 |
| 5 | Classifications-II | Lecture-5 |
| 6 | Method of Characteristics-I | Lecture-6 |
| 7 | Method of Characteristics-II | Lecture-7 |
| 8 | Existence and Uniqueness Theorem | Lecture-8 |
| 9 | Transport and Burger's Equation | Lecture-9 |
| 10 | Shockwaves and General Solution | Lecture-10 |
| 11 | Separation of Variables | Lecture-11 |
| 12 | Conservation Laws | Lecture-12 |
| 13 | Reynolds Transport Theorem | Lecture-13 |
| 14 | Reynolds Transport Theorem - Control Volume Approach | Lecture-14 |
| 15 | d'Alembert's Solution for Wave Equation | Lecture-15 |
| 16 | Volume of B(x,r) | Lecture-16 |
| 17 | Spherical Means | Lecture-17 |
| 18 | Kirchhoff's Formula | Lecture-18 |
| 19 | Wave Equation-Inhomogeneous Problem and Energy Methods | Lecture-19 |
| 20 | Laplace Equation - Fundamental Solution | Lecture-20 |
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Associate Professor
In case of any doubts, please write to panch.m@iittp.ac.in or meet me in my office room during my office hours
Disclaimer: Contents in this website may have some typos or errors. So, please use it with caution. Some corrections are spelled out during lecture hours. In case, if you find any, please write to panch.m@iittp.ac.in