# Partial Differential Equations

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Kaushik Bal
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104766)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104766)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Lecture 01 : Part A - Periodic Functions](https://invisiblenetwork.ai/learn/nptel/111104766/a6131f645ec3) (YouTube)
2. [Lecture 01 : Part B - Fourier Series: Idea](https://invisiblenetwork.ai/learn/nptel/111104766/3f23ad5b9d2f) (YouTube)
3. [Lecture 01 : Part C - Convergence of Fourier Series](https://invisiblenetwork.ai/learn/nptel/111104766/13314c4b3fe2) (YouTube)
4. [Lecture 02 : Part A - Fourier Series of Arbitrary Period](https://invisiblenetwork.ai/learn/nptel/111104766/fadf46c6cc88) (YouTube)
5. [Lecture 02 : Part B - Half Range Fourier Extension](https://invisiblenetwork.ai/learn/nptel/111104766/3d2957ef96a2) (YouTube)
6. [Lecture 02 : Part C - Addendum “Double Fourier Series”](https://invisiblenetwork.ai/learn/nptel/111104766/01b576d6006d) (YouTube)
7. [Lecture 03 : Sturm Liouville Problem: An Introduction](https://invisiblenetwork.ai/learn/nptel/111104766/9a8f36179679) (YouTube)
8. [Lecture 04 part : 1 Behavior of Regular Sturm-Liouville System](https://invisiblenetwork.ai/learn/nptel/111104766/baf28d4b1524) (YouTube)
9. [Lecture 04 Part : 2 Behavior of Regular Sturm-Liouville System Part II](https://invisiblenetwork.ai/learn/nptel/111104766/54b90d2b9559) (YouTube)
10. [Lecture 04 Part : 3 Behavior of Regular Sturm-Liouville Problem Part III](https://invisiblenetwork.ai/learn/nptel/111104766/e27038b5ca9a) (YouTube)
11. [Lecture 05 : Part 1 - Basics of Calculus](https://invisiblenetwork.ai/learn/nptel/111104766/f53dda7bfcf3) (YouTube)
12. [Lecture 05 : Part 2 - Basics of Calculus 2](https://invisiblenetwork.ai/learn/nptel/111104766/dca0943393e2) (YouTube)
13. [Lecture 06 : Introduction to PDE’s](https://invisiblenetwork.ai/learn/nptel/111104766/36d6b134df87) (YouTube)
14. [Lecture 07 : First order PDE: Classification and Construction](https://invisiblenetwork.ai/learn/nptel/111104766/46006331b830) (YouTube)
15. [Lecture 08 : Geometry of First order PDE and Method of Characteristics](https://invisiblenetwork.ai/learn/nptel/111104766/970b326704e9) (YouTube)
16. [Lecture 09 : Canonical form for First order PDE](https://invisiblenetwork.ai/learn/nptel/111104766/1a98e9ae73b2) (YouTube)
17. [Lecture 10 : Separation of Variable for First order PDE](https://invisiblenetwork.ai/learn/nptel/111104766/8ba063ac388a) (YouTube)
18. [Lecture 11 : Method of Characteristics: Existence and Uniqueness](https://invisiblenetwork.ai/learn/nptel/111104766/47115676f3f0) (YouTube)
19. [Lecture 12 : Classification of Second order Linear PDE](https://invisiblenetwork.ai/learn/nptel/111104766/fdeaccfe50f2) (YouTube)
20. [Lecture 13 : Canonical Form](https://invisiblenetwork.ai/learn/nptel/111104766/8db65fc3e2aa) (YouTube)
21. [Lecture 14 : Canonical Form Examples](https://invisiblenetwork.ai/learn/nptel/111104766/d3d97392c4ed) (YouTube)
22. [Lecture 15 : Elliptic Equations: Boundary Conditions](https://invisiblenetwork.ai/learn/nptel/111104766/b039558be58c) (YouTube)
23. [Lecture 16 : Laplace Equation: Fundamental Solution](https://invisiblenetwork.ai/learn/nptel/111104766/928cc963f468) (YouTube)
24. [Lecture 17 : Maximum Principle for Laplacian](https://invisiblenetwork.ai/learn/nptel/111104766/db456f5a10da) (YouTube)
25. [Lecture 18 : Separation of Variable Formula for Laplace Equation](https://invisiblenetwork.ai/learn/nptel/111104766/c787beb4b330) (YouTube)
26. [Lecture 19 : Poisson Equation with Dirichlet and Neumann Boundary](https://invisiblenetwork.ai/learn/nptel/111104766/21981728e7fb) (YouTube)
27. [Lecture 20 : Wave Equation: Separation of Variable](https://invisiblenetwork.ai/learn/nptel/111104766/9376382722c8) (YouTube)
28. [Lecture 21 : Wave Equation: D'Alembert Formula](https://invisiblenetwork.ai/learn/nptel/111104766/4745693e3df9) (YouTube)
29. [Lecture 22 : Nonhomogeneous Wave Equation](https://invisiblenetwork.ai/learn/nptel/111104766/9662a51c8c61) (YouTube)
30. [Lecture 23 : Heat Equation: Fundamental Solution and Maximum Principle](https://invisiblenetwork.ai/learn/nptel/111104766/a1ad6db5f9dd) (YouTube)
31. [Lecture 24 : Heat Equation: Separation of Variable and Uniqueness](https://invisiblenetwork.ai/learn/nptel/111104766/32d70862306c) (YouTube)
32. [Lecture 25 : Nonhomogeneous Equations](https://invisiblenetwork.ai/learn/nptel/111104766/896440c393a0) (YouTube)