Mission

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. 

PDE

List of Topics

Classification

Method of Characteristics

ShockWaves

Big Three PDEs

Fundamental Solution

Energy Methods

Nonlinear PDEs

Characteristic ODEs

A Few Words
About the Course

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

Introduction to PDE

Get ti know the list of topics and the list of PDEs

Course Features

42

Lectures

2

Tests

1

End Semester

5

Major Topics

Class Hours

#TopicPDF
1Monday8:00 - 8:50
2Wednesday8:00 - 8:50
3Friday8:00 - 8:50

Evaluation

#AssessmentMarksTopics
1Test 120Up to Topics Covered on 5th September 2025
2Test 220Up to Topics Covered on 8th October 2025
3End Semester60End Semester

Module 1

#TopicPDF
1Introduction, History, PrerequisitesLecture-1
2Preliminaries, What is PDE?Lecture-2
3ApplicationsLecture-3
4Classifications-ILecture-4
5Classifications-IILecture-5
6Method of Characteristics-ILecture-6
7Method of Characteristics-IILecture-7
8Existence and Uniqueness TheoremLecture-8
9Transport and Burger's EquationLecture-9

Exercise Problems

#TopicCoverage
1Exercise-1All Exam Questions
2

Few Exercises

A few simple questions

Prerequisites

ODE

%

Linear Algebra

%

Real Analysis

%

Basic Functional Analysis

%
Transport Equation Animation

Transport Equation

Craft your signature voice for online platforms.

Instructor

Dr. Panchatcharam Mariappan

Associate Professor

MA612L Partial Differential Equations

IIT Tirupati

0877-250-3358
AB1-316
panch.m@iittp.ac.in