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Course11110476632 lectures

Partial Differential Equations

Prof. Kaushik Bal · IIT Kanpur

Start with lecture 1 At NPTEL

About

The course is intended for engineering students in their 2nd/3rd year. It aims to put together the basis of partial differential equations, which are essential tools in any engineering coursework. We will develop the PDE basics by solving first and second-order equations by learning about Fourier Series and Eigen-Value problems.

Intended audience: Engineering Students

Prerequisites: Real Analysis and Several Variable Calculus

Lectures

Week 1

  1. Lecture 01 : Part A - Periodic Functions YouTube
  2. Lecture 01 : Part B - Fourier Series: Idea YouTube
  3. Lecture 01 : Part C - Convergence of Fourier Series YouTube
  4. Lecture 02 : Part A - Fourier Series of Arbitrary Period YouTube
  5. Lecture 02 : Part B - Half Range Fourier Extension YouTube
  6. Lecture 02 : Part C - Addendum “Double Fourier Series” YouTube

Week 2

  1. Lecture 03 : Sturm Liouville Problem: An Introduction YouTube
  2. Lecture 04 part : 1 Behavior of Regular Sturm-Liouville System YouTube
  3. Lecture 04 Part : 2 Behavior of Regular Sturm-Liouville System Part II YouTube
  4. Lecture 04 Part : 3 Behavior of Regular Sturm-Liouville Problem Part III YouTube

Week 3

  1. Lecture 05 : Part 1 - Basics of Calculus YouTube
  2. Lecture 05 : Part 2 - Basics of Calculus 2 YouTube
  3. Lecture 06 : Introduction to PDE’s YouTube
  4. Lecture 07 : First order PDE: Classification and Construction YouTube

Week 4

  1. Lecture 08 : Geometry of First order PDE and Method of Characteristics YouTube
  2. Lecture 09 : Canonical form for First order PDE YouTube
  3. Lecture 10 : Separation of Variable for First order PDE YouTube

Week 5

  1. Lecture 11 : Method of Characteristics: Existence and Uniqueness YouTube
  2. Lecture 12 : Classification of Second order Linear PDE YouTube
  3. Lecture 13 : Canonical Form YouTube
  4. Lecture 14 : Canonical Form Examples YouTube

Week 6

  1. Lecture 15 : Elliptic Equations: Boundary Conditions YouTube
  2. Lecture 16 : Laplace Equation: Fundamental Solution YouTube
  3. Lecture 17 : Maximum Principle for Laplacian YouTube
  4. Lecture 18 : Separation of Variable Formula for Laplace Equation YouTube

Week 7

  1. Lecture 19 : Poisson Equation with Dirichlet and Neumann Boundary YouTube
  2. Lecture 20 : Wave Equation: Separation of Variable YouTube
  3. Lecture 21 : Wave Equation: D'Alembert Formula YouTube
  4. Lecture 22 : Nonhomogeneous Wave Equation YouTube

Week 8

  1. Lecture 23 : Heat Equation: Fundamental Solution and Maximum Principle YouTube
  2. Lecture 24 : Heat Equation: Separation of Variable and Uniqueness YouTube
  3. Lecture 25 : Nonhomogeneous Equations YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Kaushik Bal
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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