# Variational Methods in Mechanics

- Institution: IISc Bangalore
- Department: Mechanical Engineering
- Taught by: Prof. Ananthasuresh, Prof. Safvan Palathingal
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/112108201)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/112108201)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec1-Part I-Classification of optimization problems and the place of Calculus of Variations in it](https://invisiblenetwork.ai/learn/nptel/112108201/77dc490a04f7) (Video)
2. [Lec2-Part II-Classification of optimization problems and the place of Calculus of Variations in it](https://invisiblenetwork.ai/learn/nptel/112108201/a256110d4533) (Video)
3. [Lec3-Part I - Genesis of Calculus of Variations](https://invisiblenetwork.ai/learn/nptel/112108201/dcccada912c4) (Video)
4. [Lec4-Part II - Genesis of Calculus of Variations](https://invisiblenetwork.ai/learn/nptel/112108201/c3da812ef696) (Video)
5. [Lec5-Part I - Formulation of Calculus of Variations problems in geometry and mechanics and design](https://invisiblenetwork.ai/learn/nptel/112108201/4416d45b8db5) (Video)
6. [Lec6-Part II - Formulation of Calculus of Variations problems in geometry and mechanics and design](https://invisiblenetwork.ai/learn/nptel/112108201/07dcdf52b754) (Video)
7. [Lec7-Part I - Unconstrained minimization in one and many variables](https://invisiblenetwork.ai/learn/nptel/112108201/7fa11a984329) (Video)
8. [Lec8-Part II - Unconstrained minimization in one and many variables](https://invisiblenetwork.ai/learn/nptel/112108201/0b079e93f240) (Video)
9. [Lec9-Part I - Constrained minimization KKT conditions](https://invisiblenetwork.ai/learn/nptel/112108201/07337e929f98) (Video)
10. [Lec10-Part II - Constrained minimization KKT conditions](https://invisiblenetwork.ai/learn/nptel/112108201/5fffc3659739) (Video)
11. [Lec11-Part I - Sufficient conditions for constrained minimization](https://invisiblenetwork.ai/learn/nptel/112108201/556796b3188b) (Video)
12. [Lec12-Part II - Sufficient conditions for constrained minimization](https://invisiblenetwork.ai/learn/nptel/112108201/7ca171cd541b) (Video)
13. [Lec13-Part I-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces](https://invisiblenetwork.ai/learn/nptel/112108201/ef403878079d) (Video)
14. [Lec14-Part II-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces](https://invisiblenetwork.ai/learn/nptel/112108201/38e85573f46f) (Video)
15. [Lec15-Function spaces and Gateaux variation](https://invisiblenetwork.ai/learn/nptel/112108201/f49b054a396d) (Video)
16. [Lec16-First variation of a functional Freche?t differential and variational derivative](https://invisiblenetwork.ai/learn/nptel/112108201/7063ab088989) (Video)
17. [Lec17-Part I-Fundamental lemma of calculus of variations and Euler Lagrange equations](https://invisiblenetwork.ai/learn/nptel/112108201/0106e08e55aa) (Video)
18. [Lec18-Part II-Fundamental lemma of calculus of variations and Euler Lagrange equations](https://invisiblenetwork.ai/learn/nptel/112108201/0289cd33384a) (Video)
19. [Lec19-Extension of Euler-Lagrange equations to multiple derivatives](https://invisiblenetwork.ai/learn/nptel/112108201/71b23031903d) (Video)
20. [Lec20-Extension of Euler-Lagrange equations to multiple functions in a functional](https://invisiblenetwork.ai/learn/nptel/112108201/0db19a36d290) (Video)
21. [Lec 21-Part I-Global Constraints in calculus of variations](https://invisiblenetwork.ai/learn/nptel/112108201/ce1e86bebd99) (Video)
22. [Lec22-Part II-Global Constraints in calculus of variations](https://invisiblenetwork.ai/learn/nptel/112108201/40b6aa3ff8aa) (Video)
23. [Lec23-Part I-Local (finite subsidiary) constrains in calculus of variations](https://invisiblenetwork.ai/learn/nptel/112108201/4340b7c963ea) (Video)
24. [Lec 24-Part II-Local (finite subsidiary) constrains in calculus of variations](https://invisiblenetwork.ai/learn/nptel/112108201/a754c3eddb9f) (Video)
25. [Lec25-Part I-Size optimization of a bar for maximum stiffness for given volume](https://invisiblenetwork.ai/learn/nptel/112108201/7c785a6f9917) (Video)
26. [Lec26-Part II-Size optimization of a bar for maximum stiffness for given volume](https://invisiblenetwork.ai/learn/nptel/112108201/b0801c843290) (Video)
27. [Lec27-Part III-Size optimization of a bar for maximum stiffness for given volume](https://invisiblenetwork.ai/learn/nptel/112108201/991b5e605c0c) (Video)
28. [Lec28-Part I-Calculus of variations in functionals involving two and three independent variables](https://invisiblenetwork.ai/learn/nptel/112108201/7ed6428c9a88) (Video)
29. [Lec29-Part II-Calculus of variations in functionals involving two and three independent variables](https://invisiblenetwork.ai/learn/nptel/112108201/533c93581456) (Video)
30. [Lec30-Part I-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions](https://invisiblenetwork.ai/learn/nptel/112108201/a516f5c8f8e2) (Video)
31. [Lec31-Part II-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions](https://invisiblenetwork.ai/learn/nptel/112108201/b80a303f1e6a) (Video)
32. [Lec32-Variational (energy) methods in statics; principles of minimum potential energy and virtual work](https://invisiblenetwork.ai/learn/nptel/112108201/a3fa225fc2ac) (Video)
33. [Lec33-Part I-General framework of optimal structural designs](https://invisiblenetwork.ai/learn/nptel/112108201/3cc05b239ff1) (Video)
34. [Lec34-Part II-General framework of optimal structural designs](https://invisiblenetwork.ai/learn/nptel/112108201/7d3da57ce5d8) (Video)
35. [Lec35-Optimal structural design of bars and beams using the optimality criteria method](https://invisiblenetwork.ai/learn/nptel/112108201/a41617645bae) (Video)
36. [Lec36-Invariants of Euler-Lagrange equations and canonical forms](https://invisiblenetwork.ai/learn/nptel/112108201/6194e1658f05) (Video)
37. [Lec37-Noether’s theorem](https://invisiblenetwork.ai/learn/nptel/112108201/c0061a164faa) (Video)
38. [Lec38-Minimum characterization of Sturm-Liouville problems](https://invisiblenetwork.ai/learn/nptel/112108201/23c16bdb5a46) (Video)
39. [Lec39-Rayleigh quotient for natural frequencies and mode shapes of elastic systems](https://invisiblenetwork.ai/learn/nptel/112108201/bb290d14ac74) (Video)
40. [Lec40-Stability analysis and buckling using calculus of variations](https://invisiblenetwork.ai/learn/nptel/112108201/6b130d092b82) (Video)
41. [Lec41-Strongest (most stable) column](https://invisiblenetwork.ai/learn/nptel/112108201/bdfe786ebb25) (Video)
42. [Lec42-Dynamic compliance optimization](https://invisiblenetwork.ai/learn/nptel/112108201/a17baa62341a) (Video)
43. [Lec43-Electro-thermal-elastic structural optimization](https://invisiblenetwork.ai/learn/nptel/112108201/b7baaa006d07) (Video)
44. [Lec44-Formulating the extremization problem starting from the differential equation, self-adjointness of the differential operator, and methods to deal with conservative and dissipative system](https://invisiblenetwork.ai/learn/nptel/112108201/77779c6df83c) (Video)