NOC:Partial Differential Equations (2025)

Lecture 1 - Periodic Functions - Part A

Lecture 2 - Fourier Series: Idea - Part B

Lecture 3 - Convergence of Fourier Series - Part C

Lecture 4 - Fourier Series of Arbitrary Period - Part A

Lecture 5 - Half Range Fourier Extension - Part B

Lecture 6 - Addendum 'Double Fourier Series' - Part C

Lecture 7 - Sturm Liouville Problem: An Introduction

Lecture 8 - Behavior of Regular Sturm-Liouville System - Part I

Lecture 9 - Behavior of Regular Sturm-Liouville System - Part II

Lecture 10 - Behavior of Regular Sturm-Liouville Problem - Part III

Lecture 11 - Basics of Calculus - Part 1

Lecture 12 - Basics of Calculus - Part 2

Lecture 13 - Introduction to PDE’s

Lecture 14 - First order PDE: Classification and Construction

Lecture 15 - Geometry of First order PDE and Method of Characteristics

Lecture 16 - Canonical form for First order PDE

Lecture 17 - Separation of Variable for First order PDE

Lecture 18 - Method of Characteristics: Existence and Uniqueness

Lecture 19 - Classification of Second order Linear PDE

Lecture 20 - Canonical Form

Lecture 21 - Canonical Form Examples

Lecture 22 - Elliptic Equations: Boundary Conditions

Lecture 23 - Laplace Equation: Fundamental Solution

Lecture 24 - Maximum Principle for Laplacian

Lecture 25 - Separation of Variable Formula for Laplace Equation

Lecture 26 - Poisson Equation with Dirichlet and Neumann Boundary

Lecture 27 - Wave Equation: Separation of Variable

Lecture 28 - Wave Equation: D'Alembert Formula

Lecture 29 - Nonhomogeneous Wave Equation

Lecture 30 - Heat Equation: Fundamental Solution and Maximum Principle

Lecture 31 - Heat Equation: Separation of Variable and Uniqueness

Lecture 32 - Nonhomogeneous Equations