# Ordinary Differential Equations and Applications

- Institution: IISc Bangalore
- Department: Mathematics
- Taught by: A. K. Nandakumaran, P. S. Datti, Raju K. George
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108081)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108081)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [General Introduction](https://invisiblenetwork.ai/learn/nptel/111108081/c45073bb9ef5) (Video)
2. [Examples](https://invisiblenetwork.ai/learn/nptel/111108081/980f15f90d2d) (Video)
3. [Examples Continued I](https://invisiblenetwork.ai/learn/nptel/111108081/ffac80051945) (Video)
4. [Examples Continued II](https://invisiblenetwork.ai/learn/nptel/111108081/67a6d166fa84) (Video)
5. [Linear Algebra](https://invisiblenetwork.ai/learn/nptel/111108081/a23bb6ed57fa) (Video)
6. [Linear Algebra Continued I](https://invisiblenetwork.ai/learn/nptel/111108081/f8e4dfce4186) (Video)
7. [Linear Algebra Continued II](https://invisiblenetwork.ai/learn/nptel/111108081/55765888b08e) (Video)
8. [Analysis](https://invisiblenetwork.ai/learn/nptel/111108081/9b1e18f6dea2) (Video)
9. [Analysis Continued](https://invisiblenetwork.ai/learn/nptel/111108081/b05830df0eba) (Video)
10. [First Order Linear Equations](https://invisiblenetwork.ai/learn/nptel/111108081/53a228be4066) (Video)
11. [Exact Equations](https://invisiblenetwork.ai/learn/nptel/111108081/397f0fa53f3f) (Video)
12. [Second Order Linear Equations](https://invisiblenetwork.ai/learn/nptel/111108081/eaff0cd5771e) (Video)
13. [Second Order Linear Equations Continued I](https://invisiblenetwork.ai/learn/nptel/111108081/79e8988be3cc) (Video)
14. [Second Order Linear Equations Continued II](https://invisiblenetwork.ai/learn/nptel/111108081/a2d4ee48b0ae) (Video)
15. [Well-posedness and Examples of IVP](https://invisiblenetwork.ai/learn/nptel/111108081/3f8c3883ac50) (Video)
16. [Gronwall's Lemma](https://invisiblenetwork.ai/learn/nptel/111108081/0147de2345db) (Video)
17. [Basic Lemma and Uniqueness Theorem](https://invisiblenetwork.ai/learn/nptel/111108081/eb4fde5132ff) (Video)
18. [Picard's Existence and Uniqueness Theorem](https://invisiblenetwork.ai/learn/nptel/111108081/36a569515b17) (Video)
19. [Picard's Existence and Uniqueness Continued](https://invisiblenetwork.ai/learn/nptel/111108081/3e02b82b4b33) (Video)
20. [Cauchy Peano Existence Theorem](https://invisiblenetwork.ai/learn/nptel/111108081/39ccb14d4ce0) (Video)
21. [Existence using Fixed Point Theorem](https://invisiblenetwork.ai/learn/nptel/111108081/b8596929b2d3) (Video)
22. [Continuation of Solutions](https://invisiblenetwork.ai/learn/nptel/111108081/572d4fe45bad) (Video)
23. [Series Solution](https://invisiblenetwork.ai/learn/nptel/111108081/7583605503f5) (Video)
24. [General System and Diagonalizability](https://invisiblenetwork.ai/learn/nptel/111108081/7efbce75d03a) (Video)
25. [2 by 2 systems and Phase Plane Analysis](https://invisiblenetwork.ai/learn/nptel/111108081/e721220d0851) (Video)
26. [2 by 2 systems and Phase Plane Analysis Continued](https://invisiblenetwork.ai/learn/nptel/111108081/e9b97ff66463) (Video)
27. [General Systems](https://invisiblenetwork.ai/learn/nptel/111108081/583b82ad3ded) (Video)
28. [General Systems Continued and Non-homogeneous Systems](https://invisiblenetwork.ai/learn/nptel/111108081/ef099b3b1f45) (Video)
29. [Basic Definitions and Examples](https://invisiblenetwork.ai/learn/nptel/111108081/1c2eb88c0360) (Video)
30. [Stability Equilibrium Points](https://invisiblenetwork.ai/learn/nptel/111108081/aef700fe52d9) (Video)
31. [Stability Equilibrium Points Continued I](https://invisiblenetwork.ai/learn/nptel/111108081/9336a7dee816) (Video)
32. [Stability Equilibrium Points Continued II](https://invisiblenetwork.ai/learn/nptel/111108081/6a9098e3b9d0) (Video)
33. [Second Order Linear Equations Continued III](https://invisiblenetwork.ai/learn/nptel/111108081/89253baa581a) (Video)
34. [Lyapunov Function](https://invisiblenetwork.ai/learn/nptel/111108081/d38532115ebc) (Video)
35. [Lyapunov Function Continued](https://invisiblenetwork.ai/learn/nptel/111108081/82b624e44020) (Video)
36. [Periodic Orbits and Poincare Bendixon Theory](https://invisiblenetwork.ai/learn/nptel/111108081/e2651cefc66b) (Video)
37. [Periodic Orbits and Poincare Bendixon Theory Continued](https://invisiblenetwork.ai/learn/nptel/111108081/a5d361ecf4e5) (Video)
38. [Linear Second Order Equations](https://invisiblenetwork.ai/learn/nptel/111108081/5ea374e1cdd0) (Video)
39. [General Second Order Equations](https://invisiblenetwork.ai/learn/nptel/111108081/7639ebef23d3) (Video)
40. [General Second Order Equations Continued](https://invisiblenetwork.ai/learn/nptel/111108081/ae2674deb73a) (Video)