# Variational Calculus and its applications in Control Theory and Nanomechanics

- Institution: IIIT Delhi
- Department: Mathematics
- Teacher: Prof. Sarthok Sircar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106144)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106144)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction / Euler Lagrange Equations - Part 1](https://invisiblenetwork.ai/learn/nptel/111106144/1e156ebc1ed3) (Video)
2. [Introduction / Euler Lagrange Equations - Part 2](https://invisiblenetwork.ai/learn/nptel/111106144/b4b5fc744c75) (Video)
3. [Introduction / Euler Lagrange Equations - Part 3](https://invisiblenetwork.ai/learn/nptel/111106144/ce46824d9da8) (Video)
4. [Introduction / Euler Lagrange Equations - Part 4](https://invisiblenetwork.ai/learn/nptel/111106144/94a0ff5a71cd) (Video)
5. [Introduction / Euler Lagrange Equations - Part 5](https://invisiblenetwork.ai/learn/nptel/111106144/82b23971a5c3) (Video)
6. [Introduction / Euler Lagrange Equations - Part 6](https://invisiblenetwork.ai/learn/nptel/111106144/1df5d520ee40) (Video)
7. [Special cases / Invariance, Existence and Uniqueness of solutions - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/8145331019c6) (Video)
8. [Special cases / Invariance, Existence and Uniqueness of solutions - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/b23bf72abebe) (Video)
9. [Special cases / Invariance, Existence and Uniqueness of solutions - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/bf4a213001a0) (Video)
10. [Special cases / Invariance, Existence and Uniqueness of solutions - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/0432a2f79ac2) (Video)
11. [Special cases / Invariance, Existence and Uniqueness of solutions - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/73d9eb08981c) (Video)
12. [Special cases / Invariance, Existence and Uniqueness of solutions - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/b1507c824339) (Video)
13. [Generalization / Numerical solution of Euler Lagrange Equations - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/1b5b99da218d) (Video)
14. [Generalization / Numerical solution of Euler Lagrange Equations - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/1b6e8d183483) (Video)
15. [Generalization / Numerical solution of Euler Lagrange Equations - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/6fb39db3ec3e) (Video)
16. [Generalization / Numerical solution of Euler Lagrange Equations - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/ed33f3bf46fc) (Video)
17. [Generalization / Numerical solution of Euler Lagrange Equations - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/ac96856aeccb) (Video)
18. [Generalization / Numerical solution of Euler Lagrange Equations - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/206162a20b6d) (Video)
19. [Isoperimetric Problems - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/089ab2eb3165) (Video)
20. [Isoperimetric Problems - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/4e2fa3ce4f22) (Video)
21. [Isoperimetric Problems - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/af608a55dd53) (Video)
22. [Isoperimetric Problems - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/174c78c42a9e) (Video)
23. [Isoperimetric Problems - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/de6b103516a9) (Video)
24. [Isoperimetric Problems - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/eb17c3bf5f86) (Video)
25. ["Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 01"](https://invisiblenetwork.ai/learn/nptel/111106144/3d56bda41a8d) (Video)
26. ["Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 02"](https://invisiblenetwork.ai/learn/nptel/111106144/5d0445d5c273) (Video)
27. ["Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 03"](https://invisiblenetwork.ai/learn/nptel/111106144/9b819fc2bb98) (Video)
28. [Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/9f1269354867) (Video)
29. [Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/401daa0e55fe) (Video)
30. [Problems with Holononomic and non- Holononomic Constraints, Variable Endpts - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/b9930ade44bf) (Video)
31. [Broken extremals / Hamiltonian Formulation - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/50412cc21910) (Video)
32. [Broken extremals / Hamiltonian Formulation - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/4215a4d516ff) (Video)
33. [Broken extremals / Hamiltonian Formulation - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/eb206b7b29d5) (Video)
34. [Broken extremals / Hamiltonian Formulation - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/a13938b3aca7) (Video)
35. [Broken extremals / Hamiltonian Formulation - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/edb0dbec2d2a) (Video)
36. [Broken extremals / Hamiltonian Formulation - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/12b2d8e114e5) (Video)
37. [Hamilton-Jacobi Equations - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/897bf830359a) (Video)
38. [Hamilton-Jacobi Equations - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/11ceff1feec5) (Video)
39. [Hamilton-Jacobi Equations - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/49a23d1efc08) (Video)
40. [Hamilton-Jacobi Equations - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/8ed52a27c6e9) (Video)
41. [Hamilton's equations, Symplectic Maps, Hamilton-Jacobi Equations, Conservative systems,](https://invisiblenetwork.ai/learn/nptel/111106144/89d5b1116a62) (Video)
42. [Hamilton-Jacobi Equations - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/ec051aef0014) (Video)
43. [Noether's Theorem / Introduction to Second Variation - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/4d51e9026da6) (Video)
44. [Noether's Theorem / Introduction to Second Variation - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/5d672da6a981) (Video)
45. [Noether's Theorem / Introduction to Second Variation - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/87d2481dfc69) (Video)
46. [Noether's Theorem / Introduction to Second Variation - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/cef2b1d94a09) (Video)
47. [Noether's Theorem / Introduction to Second Variation - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/0f7a573a48f2) (Video)
48. [Noether's Theorem / Introduction to Second Variation - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/b146c8eba4fc) (Video)
49. [Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/8fb645fd199e) (Video)
50. [Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/c97c2b376cde) (Video)
51. [Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/71c14edab9dc) (Video)
52. [Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/4f71d3f5477a) (Video)
53. [Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/c8de7eb8e9ac) (Video)
54. [Conjugate points / Jacobi Accessory Equations / Introduction to Optimal Control Theory - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/6d3e8a114ace) (Video)
55. [Constrained Optimization in Optimal Control Theory - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/75865649ab47) (Video)
56. [Constrained Optimization in Optimal Control Theory - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/33520a3b9a82) (Video)
57. [Constrained Optimization in Optimal Control Theory - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/ee6516288c32) (Video)
58. [Constrained Optimization in Optimal Control Theory - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/f155f0fcadb8) (Video)
59. [Constrained Optimization in Optimal Control Theory - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/b24bb62239c2) (Video)
60. [Constrained Optimization in Optimal Control Theory - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/6cf4da0d8c05) (Video)
61. [Introduction to Nanomechanics - Part 01](https://invisiblenetwork.ai/learn/nptel/111106144/2aa4fb555041) (Video)
62. [Introduction to Nanomechanics - Part 02](https://invisiblenetwork.ai/learn/nptel/111106144/e8634cfdd6dd) (Video)
63. [Introduction to Nanomechanics - Part 03](https://invisiblenetwork.ai/learn/nptel/111106144/eb61552e0590) (Video)
64. [Introduction to Nanomechanics - Part 04](https://invisiblenetwork.ai/learn/nptel/111106144/6985a8e41eaf) (Video)
65. [Introduction to Nanomechanics - Part 05](https://invisiblenetwork.ai/learn/nptel/111106144/6aa3799435df) (Video)
66. [Introduction to Nanomechanics - Part 06](https://invisiblenetwork.ai/learn/nptel/111106144/93c11b8d9748) (Video)
67. [Live Session 27-02-2021](https://invisiblenetwork.ai/learn/nptel/111106144/1e156ebc1ed3-2) (Video)
68. [Live Session 13-02-2022](https://invisiblenetwork.ai/learn/nptel/111106144/b4b5fc744c75-2) (Video)
69. [Live Session 29-03-2022](https://invisiblenetwork.ai/learn/nptel/111106144/ce46824d9da8-2) (Video)