# Ordinary Differential Equations

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Kaushik Bal
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104521)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104521)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Differential Equations are one of the central topics which results when studying models arising out of physical systems. Most often than not the nonlinear nature of the equation forces us to study the qualitative and geometric theory of equations and dynamical systems. In this course we start by first studying about the various aspect of Linear Systems and then analyze local and global behavior of nonlinear systems using techniques from Linear theory.

Intended audience: Undergraduate students in Mathematics, Physics and Engineering, Graduate students in Mathematics.

Prerequisites: Linear Algebra and Several Variable Calculus.

## Lectures

1. [Lecture 1, Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111104521/9db655fd3fd3) (YouTube)
2. [Lecture 2, Linear Transformations](https://invisiblenetwork.ai/learn/nptel/111104521/f29d78119753) (YouTube)
3. [Lecture 3, Matrices](https://invisiblenetwork.ai/learn/nptel/111104521/6a4cacb4c817) (YouTube)
4. [Lecture 4, Derivatives](https://invisiblenetwork.ai/learn/nptel/111104521/fc83ed024907) (YouTube)
5. [Lecture 5, Lipschitz Continuity](https://invisiblenetwork.ai/learn/nptel/111104521/71db6a043efb) (YouTube)
6. [Lecture 6, Cauchy Schwartz Inequality](https://invisiblenetwork.ai/learn/nptel/111104521/4a25154e2397) (YouTube)
7. [Lecture-7, Ordinary Differential Equations: Introduction](https://invisiblenetwork.ai/learn/nptel/111104521/49883a671ce4) (YouTube)
8. [Lecture-8, Differential Inequalities](https://invisiblenetwork.ai/learn/nptel/111104521/f5700d54d7f4) (YouTube)
9. [Lecture-9, 2nd Order ODEs](https://invisiblenetwork.ai/learn/nptel/111104521/7f0a1e57f3a9) (YouTube)
10. [Lecture-10, Picard's Theorem](https://invisiblenetwork.ai/learn/nptel/111104521/eedf2721c471) (YouTube)
11. [Lecture-11, Linear Dependence and Independence](https://invisiblenetwork.ai/learn/nptel/111104521/89cf1c73b25f) (YouTube)
12. [Lecture 12, Well-posedness of an ODE](https://invisiblenetwork.ai/learn/nptel/111104521/3518ef9be393) (YouTube)
13. [Lecture 13, Linear System 1](https://invisiblenetwork.ai/learn/nptel/111104521/a08691be30df) (YouTube)
14. [Lecture 14, Linear System 2](https://invisiblenetwork.ai/learn/nptel/111104521/f7eef36a7879) (YouTube)
15. [Extra Lecture](https://invisiblenetwork.ai/learn/nptel/111104521/a30edaf56c39) (YouTube)
16. [Lecture 15, Exponential matrix](https://invisiblenetwork.ai/learn/nptel/111104521/d50d9bdd40aa) (YouTube)
17. [Lecture 16, Solution of linear system system of ODE](https://invisiblenetwork.ai/learn/nptel/111104521/98f99a08db0b) (YouTube)
18. [Lecture 17, Eigen value and eigen vector](https://invisiblenetwork.ai/learn/nptel/111104521/9772d035fde7) (YouTube)
19. [Lecture 18, Canonical form](https://invisiblenetwork.ai/learn/nptel/111104521/3a59f55d63d3) (YouTube)
20. [Lecture 19, Solution of system of equations using method of eigenvalue](https://invisiblenetwork.ai/learn/nptel/111104521/02b30f5ededf) (YouTube)
21. [Lecture 20, Method of eigenvalue continued](https://invisiblenetwork.ai/learn/nptel/111104521/fb4deb9c0836) (YouTube)
22. [Lecture 21, Maximal interval of existence](https://invisiblenetwork.ai/learn/nptel/111104521/a030c94b254d) (YouTube)
23. [Lecture 22, Maximal interval of existence continued](https://invisiblenetwork.ai/learn/nptel/111104521/12b66ce83766) (YouTube)
24. [Lecture 23, Periodic Linear system](https://invisiblenetwork.ai/learn/nptel/111104521/70741f554050) (YouTube)
25. [Lecture 24, Asymptotic behavior of solution](https://invisiblenetwork.ai/learn/nptel/111104521/6a1c40f4852d) (YouTube)
26. [Lecture 25, Asymptotic behavior of solution( continued )](https://invisiblenetwork.ai/learn/nptel/111104521/f7aa09a35c7c) (YouTube)
27. [Lecture 26, Asymptotic Behavior of Linear System: Part 3](https://invisiblenetwork.ai/learn/nptel/111104521/bad80b78a032) (YouTube)
28. [Lecture 27, Exact and Adjoint Equation](https://invisiblenetwork.ai/learn/nptel/111104521/adee11e6977a) (YouTube)
29. [Lecture 28, Theory of Oscillation](https://invisiblenetwork.ai/learn/nptel/111104521/2c2421b55cda) (YouTube)
30. [Lecture 29: Sturm-Picone's theorem, Leighton's theorem](https://invisiblenetwork.ai/learn/nptel/111104521/f76b498f5035) (YouTube)
31. [Lecture 30: Boundary Value Problems](https://invisiblenetwork.ai/learn/nptel/111104521/741a05d0951a) (YouTube)
32. [Lecture 31: Maximum Principle](https://invisiblenetwork.ai/learn/nptel/111104521/e640630f6299) (YouTube)
33. [Lecture 32, Strum-Liouville Theory](https://invisiblenetwork.ai/learn/nptel/111104521/39c0bb605d97) (YouTube)
34. [Lecture 33, Strum-Liouville Theory 2](https://invisiblenetwork.ai/learn/nptel/111104521/616fb845fb4a) (YouTube)
35. [Lecture 34, Periodic Strum-Liouville Problem](https://invisiblenetwork.ai/learn/nptel/111104521/be058653bb36) (YouTube)
36. [Lecture 35, Eigenfunction Expansion](https://invisiblenetwork.ai/learn/nptel/111104521/205c2799c9ed) (YouTube)
37. [Lecture 36, Stability of a system](https://invisiblenetwork.ai/learn/nptel/111104521/dabb7e91401e) (YouTube)
38. [Lecture 37, Equilibrium points](https://invisiblenetwork.ai/learn/nptel/111104521/870f946d627a) (YouTube)
39. [Lecture 38, Lyapunov function and its application](https://invisiblenetwork.ai/learn/nptel/111104521/3d989a34aa61) (YouTube)
40. [Lecture 39, Stability of Equilibria](https://invisiblenetwork.ai/learn/nptel/111104521/d16ec1d68070) (YouTube)
41. [Lecture 40, Phase Portrait](https://invisiblenetwork.ai/learn/nptel/111104521/a3f4c239e888) (YouTube)