# Ordinary Differential Equations : Power series, eigenvalues and Green functions

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. Somnath Bhattacharyya
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105003)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105003)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Ordinary Differential equations (ODE) are useful to analyze any physical phenomena. Solution techniques for differential equations are thus, very important aspects in mathematics and engineering. In this course the series solution of several typical ODEs in the form of Legendre polynomials, Bessel functions, Hermit polynomials etc. will be illustrated. The Eigen function solution and Greens function for the non-homogeneous boundary value problems will be introduced. This course provides techniques for solving ODEs, which will not only serve as UG/PG core course on Mathematical Methods/ Engineering Mathematics, it also be useful for preparing GATE examination in Mathematics. There is no such online course which provides in a short form on analytical tools to solve homogeneous as well as non-homogeneous ODEs starting from the basics.

Intended audience: Any interested students can take this course

Prerequisites: Basic calculus

## Lectures

1. [Lecture 01: Introduction to ODE, IVP, BVP and conversion of IVP to first order ODE](https://invisiblenetwork.ai/learn/nptel/111105003/44a656925a10) (YouTube)
2. [Lecture 02: Existance and uniqueness of solution, Lipschitz Function](https://invisiblenetwork.ai/learn/nptel/111105003/cb796665d58b) (YouTube)
3. [Lecture 03: Picard Method of Successive Approximations](https://invisiblenetwork.ai/learn/nptel/111105003/872e5ec6ff6a) (YouTube)
4. [Lecture 04: Systems of first-order ODEs, Eigenvalues and eigenvectors](https://invisiblenetwork.ai/learn/nptel/111105003/387ad76e5e52) (YouTube)
5. [Lecture 05: Introduction to Linear Stability Analysis](https://invisiblenetwork.ai/learn/nptel/111105003/d808b5500153) (YouTube)
6. [Lecture 06: Series solution of ODE, ordinary point](https://invisiblenetwork.ai/learn/nptel/111105003/686fe5c830af) (YouTube)
7. [Lecture 07: Legendre Polynomial](https://invisiblenetwork.ai/learn/nptel/111105003/4c5952786a5e) (YouTube)
8. [Lecture 08: Recursion relation of Legendre polynomials](https://invisiblenetwork.ai/learn/nptel/111105003/a6d4d3a6c3a2) (YouTube)
9. [Lecture 09: Rodrigues Formula and Orthogonality of Legendre Polynomial](https://invisiblenetwork.ai/learn/nptel/111105003/f6e91ae5d0d7) (YouTube)
10. [Lecture 10: Properties of Legendre Polynomial](https://invisiblenetwork.ai/learn/nptel/111105003/3861825dd826) (YouTube)
11. [Lecture 11: Generating Function](https://invisiblenetwork.ai/learn/nptel/111105003/4b88ea52c66f) (YouTube)
12. [Lecture 12: Singular Point and Frobenius Series](https://invisiblenetwork.ai/learn/nptel/111105003/401483f7f0a6) (YouTube)
13. [Lecture 13: Bessel function and Recurrence Relation](https://invisiblenetwork.ai/learn/nptel/111105003/42a2f955b535) (YouTube)
14. [Lecture 14: Properties of Bessel Functions and Reduciable to Bessel Equation](https://invisiblenetwork.ai/learn/nptel/111105003/3a17ccad5102) (YouTube)
15. [Lecture 15: Boundary Value Problems, Self-adjoint Differential Operator](https://invisiblenetwork.ai/learn/nptel/111105003/7dc57ec6dccf) (YouTube)
16. [Lecture 16: Eigenfunction and eigenvalues of self adjoint operator](https://invisiblenetwork.ai/learn/nptel/111105003/c93fa104b332) (YouTube)
17. [Lecture 17: Orthogonality of Eigenfunctions](https://invisiblenetwork.ai/learn/nptel/111105003/6ff9d6940797) (YouTube)
18. [Lecture 18: Sturm-Liouville Problem and Eigenfunction Expansion Technique](https://invisiblenetwork.ai/learn/nptel/111105003/11ffe162495f) (YouTube)
19. [Lecture 19: Derac Delta Function and Green's Function](https://invisiblenetwork.ai/learn/nptel/111105003/d2d7bd193c15) (YouTube)
20. [Lecture 20: Green's Function for ODE](https://invisiblenetwork.ai/learn/nptel/111105003/fb55f6e619ed) (YouTube)