# Mathematical Methods In Physics 2

- Institution: IISER Bhopal
- Department: Mathematics
- Teacher: Prof. Auditya Sharma
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106152)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106152)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This would be the second of a two-part series on Mathematical Methods in Physics. The aim here is to provide a solid mathematical foundation for the budding Physicist eager to climb the ladder of self-learning. This course is designed to cater to an undergraduate student who excitedly embarks on a study of Physics, but is obstructed by the mathematics which appears so forbidding. The approach we will follow is one of showing many examples, and weaving the theory around examples. When possible, we will show how Mathematica can be used to offer extra insight.

Intended audience: Any Interested Learners

Prerequisites: We try to make this self-contained. However,some familiarity with the basic mathematical tools used in say, the first courses on Mechanics, Electromagnetism, would help.INDUSTRIES SUPPORT : Quantitative Finance and Scientific consulting companies

## Lectures

1. [Introduction to complex numbers](https://invisiblenetwork.ai/learn/nptel/111106152/93e9eeead6c8) (YouTube)
2. [The triangle inequality](https://invisiblenetwork.ai/learn/nptel/111106152/f549de7a2fe8) (YouTube)
3. [The de Moivre formula](https://invisiblenetwork.ai/learn/nptel/111106152/0514d5c643b3) (YouTube)
4. [Roots of unity](https://invisiblenetwork.ai/learn/nptel/111106152/a9c25c7ea564) (YouTube)
5. [Functions of a complex variable and the notion of continuity](https://invisiblenetwork.ai/learn/nptel/111106152/c6469b6ea28e) (YouTube)
6. [Derivative of a complex function](https://invisiblenetwork.ai/learn/nptel/111106152/d205ce72ca88) (YouTube)
7. [Differentiation rules for a complex function](https://invisiblenetwork.ai/learn/nptel/111106152/69e79cd628e2) (YouTube)
8. [Cauchy-Riemann Equations](https://invisiblenetwork.ai/learn/nptel/111106152/9c8565c37c46) (YouTube)
9. [Sufficient conditions for differentiability](https://invisiblenetwork.ai/learn/nptel/111106152/d3b00e505ea8) (YouTube)
10. [Cauchy-Riemann conditions in polar coordinates](https://invisiblenetwork.ai/learn/nptel/111106152/0b81c534bfa6) (YouTube)
11. [More persepective on differentiability](https://invisiblenetwork.ai/learn/nptel/111106152/2207c1f5b410) (YouTube)
12. [The value of the derivative](https://invisiblenetwork.ai/learn/nptel/111106152/ea99b2a13ce5) (YouTube)
13. [Analytic functions](https://invisiblenetwork.ai/learn/nptel/111106152/f83566758828) (YouTube)
14. [Harmonic functions](https://invisiblenetwork.ai/learn/nptel/111106152/263c9ad1cfd6) (YouTube)
15. [The exponential function](https://invisiblenetwork.ai/learn/nptel/111106152/a50a91e533e6) (YouTube)
16. [Complex logarithm](https://invisiblenetwork.ai/learn/nptel/111106152/d3c82d7fa375) (YouTube)
17. [Complex exponents](https://invisiblenetwork.ai/learn/nptel/111106152/d8548f0d8aa9) (YouTube)
18. [Trigonometric functions of complex variables](https://invisiblenetwork.ai/learn/nptel/111106152/04baab611242) (YouTube)
19. [Hyperbolic functions of complex variables](https://invisiblenetwork.ai/learn/nptel/111106152/bef0c18124a6) (YouTube)
20. [Inverse Trigonometric and Hyperbolic functions](https://invisiblenetwork.ai/learn/nptel/111106152/db5f6c038e79) (YouTube)
21. [Branch of a multivalued function](https://invisiblenetwork.ai/learn/nptel/111106152/3298f73822ea) (YouTube)
22. [Contour Integrals](https://invisiblenetwork.ai/learn/nptel/111106152/20b46e55f3ad) (YouTube)
23. [Green's Theorem](https://invisiblenetwork.ai/learn/nptel/111106152/fbbed0b7e9e6) (YouTube)
24. [Path dependence of the contour intergal](https://invisiblenetwork.ai/learn/nptel/111106152/de966918aaed) (YouTube)
25. [Antiderivatives](https://invisiblenetwork.ai/learn/nptel/111106152/250c98c329db) (YouTube)
26. [The Cauchy theorem](https://invisiblenetwork.ai/learn/nptel/111106152/dbfdd19e52e4) (YouTube)
27. [Crossing contours and multiply connected domains](https://invisiblenetwork.ai/learn/nptel/111106152/f6e2619e6076) (YouTube)
28. [Cauchy Integral formula](https://invisiblenetwork.ai/learn/nptel/111106152/e9ec07cad083) (YouTube)
29. [Derivatives of an analytic function](https://invisiblenetwork.ai/learn/nptel/111106152/4ec8f99f4309) (YouTube)
30. [Liouville's theorem and the Fundamental theorem of algebra](https://invisiblenetwork.ai/learn/nptel/111106152/63f28a034540) (YouTube)
31. [Taylor Series](https://invisiblenetwork.ai/learn/nptel/111106152/aeace80f85e3) (YouTube)
32. [Laurent Series](https://invisiblenetwork.ai/learn/nptel/111106152/9a992eaf1c9c) (YouTube)
33. [Convergence](https://invisiblenetwork.ai/learn/nptel/111106152/20bd9b8d75d9) (YouTube)
34. [Differentiation and integration of power series](https://invisiblenetwork.ai/learn/nptel/111106152/43f5886645e4) (YouTube)
35. [Isolated Singularities](https://invisiblenetwork.ai/learn/nptel/111106152/9ae5bf4a6017) (YouTube)
36. [Residues](https://invisiblenetwork.ai/learn/nptel/111106152/3ca9ed215886) (YouTube)
37. [Residue Theorem](https://invisiblenetwork.ai/learn/nptel/111106152/a7c778206509) (YouTube)
38. [Evaluation of integrals-I](https://invisiblenetwork.ai/learn/nptel/111106152/ca16cc696e17) (YouTube)
39. [Evaluation of integrals-II](https://invisiblenetwork.ai/learn/nptel/111106152/4c226133abca) (YouTube)
40. [Analytic Continuation](https://invisiblenetwork.ai/learn/nptel/111106152/8abb866fbb6d) (YouTube)
41. [Introduction of orthogonal polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/2ee7dc8e09ab) (YouTube)
42. [How to construct orthogonal polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/8e511f1b5fd6) (YouTube)
43. [The weight function](https://invisiblenetwork.ai/learn/nptel/111106152/051c3e30230c) (YouTube)
44. [Recursion relations](https://invisiblenetwork.ai/learn/nptel/111106152/9ff079946e0b) (YouTube)
45. [Differential equation satisfied by the orthogonal polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/a3494f1de455) (YouTube)
46. [Hermite polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/64ed9f9a4dd3) (YouTube)
47. [Properties of Hemite polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/788409cdc26a) (YouTube)
48. [Legendre polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/315f54f56c8b) (YouTube)
49. [Legendre polynomials: recurrence relation](https://invisiblenetwork.ai/learn/nptel/111106152/90a058df115d) (YouTube)
50. [Differential equation corresponding to Legendre polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/d1b863478549) (YouTube)
51. [The generating function corresponding to Legendre polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/f4b574ca4eb3) (YouTube)
52. [Laguerre Polynomials](https://invisiblenetwork.ai/learn/nptel/111106152/6d659e4c3978) (YouTube)
53. [Laguerre Polynomials: recurrence relation](https://invisiblenetwork.ai/learn/nptel/111106152/01eeb99cc31f) (YouTube)
54. [Laguerre polynomials: differential equation](https://invisiblenetwork.ai/learn/nptel/111106152/2b7bd54eb0c8) (YouTube)
55. [Laguerre polynomials: generating function](https://invisiblenetwork.ai/learn/nptel/111106152/ffba9a8e0cc2) (YouTube)
56. [Bessel functions: series defination](https://invisiblenetwork.ai/learn/nptel/111106152/07e39508e1fe) (YouTube)
57. [Bessel functions: recurrence relations](https://invisiblenetwork.ai/learn/nptel/111106152/5fad29d0fc2f) (YouTube)
58. [Bessel functions: differential equation](https://invisiblenetwork.ai/learn/nptel/111106152/e5c1be84b1fa) (YouTube)
59. [Bessel functions of integral order: generating function](https://invisiblenetwork.ai/learn/nptel/111106152/5528faf4a98c) (YouTube)
60. [Bessel function: orthogonality](https://invisiblenetwork.ai/learn/nptel/111106152/a3cfc11029f8) (YouTube)
61. [Classification of Second Order PDEs](https://invisiblenetwork.ai/learn/nptel/111106152/4b9a75d1d22d) (YouTube)
62. [Canonical Forms for Hyperbolic PDEs](https://invisiblenetwork.ai/learn/nptel/111106152/87b030170fbe) (YouTube)
63. [Canonical Forms for Parabolic PDEs](https://invisiblenetwork.ai/learn/nptel/111106152/7f40d0a04738) (YouTube)
64. [Canonical Forms for Elliptic PDEs](https://invisiblenetwork.ai/learn/nptel/111106152/fed8defa5a52) (YouTube)
65. [Tha Laplace Equation](https://invisiblenetwork.ai/learn/nptel/111106152/020a03a80464) (YouTube)
66. [The Laplace Equation: Separation of Variables](https://invisiblenetwork.ai/learn/nptel/111106152/a1cee4637d2d) (YouTube)
67. [The Laplace Equation: Dirichlet and Neumann boundary conditions](https://invisiblenetwork.ai/learn/nptel/111106152/aaa36c17050f) (YouTube)
68. [The Laplace Equation in Cartesian coordinates](https://invisiblenetwork.ai/learn/nptel/111106152/5304c89db5fd) (YouTube)
69. [The Laplace Equation for a 3-D rectangular box](https://invisiblenetwork.ai/learn/nptel/111106152/3b47c8e4e1c2) (YouTube)
70. [The Laplace Equation in spherical coordinates](https://invisiblenetwork.ai/learn/nptel/111106152/587891a8c8ea) (YouTube)
71. [The Laplace Equation in Spherical Coordinates: Solution](https://invisiblenetwork.ai/learn/nptel/111106152/1f2bf0a720a9) (YouTube)
72. [The Laplace Equation in Spherical Coordinates: illustrative examples](https://invisiblenetwork.ai/learn/nptel/111106152/b6bb8f9b6e32) (YouTube)
73. [The Poisson's Equation: Green's function solution](https://invisiblenetwork.ai/learn/nptel/111106152/937b383b6481) (YouTube)
74. [The heat equation: a heuristic discussion](https://invisiblenetwork.ai/learn/nptel/111106152/c77f765e6c23) (YouTube)
75. [From the random walk to the diffusion equation](https://invisiblenetwork.ai/learn/nptel/111106152/f1c669ff4434) (YouTube)
76. [Solution of the Diffusion equation](https://invisiblenetwork.ai/learn/nptel/111106152/9739b1f3d798) (YouTube)
77. [The Diffusion equation with Dirichlet and Neumann boundary conditions](https://invisiblenetwork.ai/learn/nptel/111106152/606f232520b6) (YouTube)
78. [The Heat equation: illustrative examples](https://invisiblenetwork.ai/learn/nptel/111106152/fe990588e867) (YouTube)
79. [The Wave equation: Method of characteristics](https://invisiblenetwork.ai/learn/nptel/111106152/8e0b8dcb5571) (YouTube)
80. [The Wave equation: Separation of variables](https://invisiblenetwork.ai/learn/nptel/111106152/a3ee718c73db) (YouTube)