# Mathematical Methods in Physics 1

- Institution: IISER Bhopal
- Department: Mathematics
- Teacher: Prof. Auditya Sharma
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106148)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106148)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Vectors](https://invisiblenetwork.ai/learn/nptel/111106148/6d35fc764038) (Video)
2. [Linear vector spaces](https://invisiblenetwork.ai/learn/nptel/111106148/b59198f6ad96) (Video)
3. [Linear vector spaces: immediate consequences](https://invisiblenetwork.ai/learn/nptel/111106148/34a34199769a) (Video)
4. [Dot product of Euclidean vectors](https://invisiblenetwork.ai/learn/nptel/111106148/345e0b34bbaa) (Video)
5. [Inner product on a Linear vector space](https://invisiblenetwork.ai/learn/nptel/111106148/b40f2a89db56) (Video)
6. [Cauchy-Schwartz inequality for Euclidean vectors](https://invisiblenetwork.ai/learn/nptel/111106148/bcbcf2bf4a1b) (Video)
7. [Cauchy-Schwartz inequality for vectors from LVS](https://invisiblenetwork.ai/learn/nptel/111106148/f148fb49efdc) (Video)
8. [Applications of the Cauchy-Schwartz inequality](https://invisiblenetwork.ai/learn/nptel/111106148/7f1e69fb3066) (Video)
9. [Triangle inequality](https://invisiblenetwork.ai/learn/nptel/111106148/7a93fd6f25d0) (Video)
10. [Linear dependence and independence of vectors](https://invisiblenetwork.ai/learn/nptel/111106148/332aa2823cd5) (Video)
11. [Row reduction of matrices](https://invisiblenetwork.ai/learn/nptel/111106148/6a6f4c6920bb) (Video)
12. [Rank of a matrix](https://invisiblenetwork.ai/learn/nptel/111106148/735d1f1b9b73) (Video)
13. [Rank of a matrix: consequences](https://invisiblenetwork.ai/learn/nptel/111106148/352f587638d6) (Video)
14. [Determinants and their properties](https://invisiblenetwork.ai/learn/nptel/111106148/62ffea106cad) (Video)
15. [The rank of a matrix using determinants](https://invisiblenetwork.ai/learn/nptel/111106148/d86df06d06d6) (Video)
16. [Cramer's rule](https://invisiblenetwork.ai/learn/nptel/111106148/3a355443375b) (Video)
17. [Square system of equations](https://invisiblenetwork.ai/learn/nptel/111106148/15e55f3ca4b8) (Video)
18. [Homogeneous equations](https://invisiblenetwork.ai/learn/nptel/111106148/c8561e3f29c7) (Video)
19. [The rank of a matrix and linear dependence](https://invisiblenetwork.ai/learn/nptel/111106148/e32f821cfbe3) (Video)
20. [Span, basis, and dimension of a LVS](https://invisiblenetwork.ai/learn/nptel/111106148/435c843009db) (Video)
21. [Gram-Schmidt orthogonalization](https://invisiblenetwork.ai/learn/nptel/111106148/3198a659906c) (Video)
22. [Vector subspaces](https://invisiblenetwork.ai/learn/nptel/111106148/dc29da88f35f) (Video)
23. [Linear operators](https://invisiblenetwork.ai/learn/nptel/111106148/92b6894ac350) (Video)
24. [Inverse of an operator](https://invisiblenetwork.ai/learn/nptel/111106148/f7e5c89e1d28) (Video)
25. [Adjoint of an operator](https://invisiblenetwork.ai/learn/nptel/111106148/e0b3224839fe) (Video)
26. [Projection operators](https://invisiblenetwork.ai/learn/nptel/111106148/691b91cbe965) (Video)
27. [Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111106148/dcf2df7e548f) (Video)
28. [Hermitian operators](https://invisiblenetwork.ai/learn/nptel/111106148/e78f92506b3e) (Video)
29. [Unitary operators](https://invisiblenetwork.ai/learn/nptel/111106148/c3e3302eb44a) (Video)
30. [Normal operators](https://invisiblenetwork.ai/learn/nptel/111106148/8f5b218bc8d4) (Video)
31. [Similarity and Unitary transformations](https://invisiblenetwork.ai/learn/nptel/111106148/1c38e6f0d857) (Video)
32. [Matrix representations](https://invisiblenetwork.ai/learn/nptel/111106148/61d539c592e6) (Video)
33. [Eigenvalues and Eigenvectors of matrices](https://invisiblenetwork.ai/learn/nptel/111106148/c9613d65a340) (Video)
34. [Defective matrices](https://invisiblenetwork.ai/learn/nptel/111106148/01868f66351c) (Video)
35. [Eigenvalues and eigenvectors: useful results](https://invisiblenetwork.ai/learn/nptel/111106148/ce4ae4b7c521) (Video)
36. [A class of invertible matrices](https://invisiblenetwork.ai/learn/nptel/111106148/d984b7e60c28) (Video)
37. [Diagonalization of matrices](https://invisiblenetwork.ai/learn/nptel/111106148/35d52892f845) (Video)
38. [Diagonalizability of matrices](https://invisiblenetwork.ai/learn/nptel/111106148/48ac53b66475) (Video)
39. [Functions of matrices](https://invisiblenetwork.ai/learn/nptel/111106148/7db188b083e7) (Video)
40. [SHM and waves](https://invisiblenetwork.ai/learn/nptel/111106148/52ce07f4d88b) (Video)
41. [Periodic functions](https://invisiblenetwork.ai/learn/nptel/111106148/f1fd6ad97c85) (Video)
42. [Average value of a function](https://invisiblenetwork.ai/learn/nptel/111106148/f60bf12188d0) (Video)
43. [Piecewise continuous functions](https://invisiblenetwork.ai/learn/nptel/111106148/a8eb49704968) (Video)
44. [Orthogonal basis: Fourier series](https://invisiblenetwork.ai/learn/nptel/111106148/e509e7a5167b) (Video)
45. [Fourier coefficients](https://invisiblenetwork.ai/learn/nptel/111106148/1efcb47b03ce) (Video)
46. [Dirichlet Conditions](https://invisiblenetwork.ai/learn/nptel/111106148/aeb6763349d5) (Video)
47. [Complex Form of Fourier Series](https://invisiblenetwork.ai/learn/nptel/111106148/5d63ebff327b) (Video)
48. [Other intervals: arbitrary period](https://invisiblenetwork.ai/learn/nptel/111106148/d45b2a28fbba) (Video)
49. [Even and Odd Functions](https://invisiblenetwork.ai/learn/nptel/111106148/f66483d7d72c) (Video)
50. [Differentiating Fourier series](https://invisiblenetwork.ai/learn/nptel/111106148/6ad36e9cad62) (Video)
51. [Parseval's theorem](https://invisiblenetwork.ai/learn/nptel/111106148/3e3c144e1877) (Video)
52. [Fourier series to Fourier transforms](https://invisiblenetwork.ai/learn/nptel/111106148/68b7fce84413) (Video)
53. [Fourier Sine and Cosine transforms](https://invisiblenetwork.ai/learn/nptel/111106148/c44108ec1ca8) (Video)
54. [Parseval's theorem for Fourier series](https://invisiblenetwork.ai/learn/nptel/111106148/ae5bf75a8514) (Video)
55. [Ordinary Differential equations](https://invisiblenetwork.ai/learn/nptel/111106148/e1a42fe255f8) (Video)
56. [First order ODEs](https://invisiblenetwork.ai/learn/nptel/111106148/038e6f6c0f4d) (Video)
57. [Linear first order ODEs](https://invisiblenetwork.ai/learn/nptel/111106148/50c01478bcdb) (Video)
58. [Orthogonal Trajectories](https://invisiblenetwork.ai/learn/nptel/111106148/821ec665dc4d) (Video)
59. [Exact differential equations](https://invisiblenetwork.ai/learn/nptel/111106148/495116b9a1ed) (Video)
60. [Special first order ODEs](https://invisiblenetwork.ai/learn/nptel/111106148/297b5de3b04b) (Video)
61. [Solutions of linear first-order ODEs](https://invisiblenetwork.ai/learn/nptel/111106148/06b4a3c9a33b) (Video)
62. [Revisit linear first-order ODEs](https://invisiblenetwork.ai/learn/nptel/111106148/9083ef2c19b0) (Video)
63. [ODEs in disguise](https://invisiblenetwork.ai/learn/nptel/111106148/ec8caeb4dd11) (Video)
64. [2nd order Homogeneous linear equations with constant coefficients](https://invisiblenetwork.ai/learn/nptel/111106148/3ab17f0a5b5f) (Video)
65. [The use of a known solution to find another](https://invisiblenetwork.ai/learn/nptel/111106148/327b14e5a6bb) (Video)
66. [An alternate approach to auxiliary equation](https://invisiblenetwork.ai/learn/nptel/111106148/8b18e0e4c26f) (Video)
67. [Inhomogeneous second order equations](https://invisiblenetwork.ai/learn/nptel/111106148/33f4e6612412) (Video)
68. [Methods to find a Particular solution](https://invisiblenetwork.ai/learn/nptel/111106148/28a562f02237) (Video)
69. [Successive Integration of two first order equations](https://invisiblenetwork.ai/learn/nptel/111106148/62d7ec9a81be) (Video)
70. [Illustrative examples.](https://invisiblenetwork.ai/learn/nptel/111106148/e48c90601beb) (Video)
71. [Variation of Parameters](https://invisiblenetwork.ai/learn/nptel/111106148/198e81dfb4f7) (Video)
72. [Vibrations in mechanical systems.](https://invisiblenetwork.ai/learn/nptel/111106148/dc99c73a74c8) (Video)
73. [Forced Vibrations.](https://invisiblenetwork.ai/learn/nptel/111106148/94481fdae9a7) (Video)
74. [Resonance](https://invisiblenetwork.ai/learn/nptel/111106148/e9bc2e18ff1b) (Video)
75. [Linear Superposition](https://invisiblenetwork.ai/learn/nptel/111106148/d8d4862d0ad1) (Video)
76. [Laplace Transform (LT)](https://invisiblenetwork.ai/learn/nptel/111106148/a2164b06eb51) (Video)
77. [Basic Properties of Laplace Transforms](https://invisiblenetwork.ai/learn/nptel/111106148/ba7a88a005b5) (Video)
78. [Step functions, Translations, and Periodic functions](https://invisiblenetwork.ai/learn/nptel/111106148/d51de7e0b39e) (Video)
79. [The Inverse Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111106148/ecc1c1b87985) (Video)
80. [Convolution of functions](https://invisiblenetwork.ai/learn/nptel/111106148/fde15a7fe856) (Video)
81. [Solving ODEs using Laplace transforms](https://invisiblenetwork.ai/learn/nptel/111106148/19928218e14a) (Video)
82. [The Dirac Delta function](https://invisiblenetwork.ai/learn/nptel/111106148/d43500f87d01) (Video)
83. [Properties of the Dirac Delta function](https://invisiblenetwork.ai/learn/nptel/111106148/9866523cd262) (Video)
84. [Green's function method](https://invisiblenetwork.ai/learn/nptel/111106148/b1a53c114251) (Video)
85. [Green's function method: Boundary value problem](https://invisiblenetwork.ai/learn/nptel/111106148/d3995b319823) (Video)
86. [Power series method](https://invisiblenetwork.ai/learn/nptel/111106148/925b1cedc4e8) (Video)
87. [Power series solutions about an ordinary point](https://invisiblenetwork.ai/learn/nptel/111106148/f36e9b2cb916) (Video)
88. [Initial value problem: power series solution](https://invisiblenetwork.ai/learn/nptel/111106148/a29a43678b30) (Video)
89. [Frobenius method for regular singular points](https://invisiblenetwork.ai/learn/nptel/111106148/0b7ae690e5e2) (Video)