Modules / Lectures

Module Name | Download |
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Assignment 1 | Assignment 1 |

Assignment 1 Solutions | Assignment 1 Solutions |

Assignment 2 | Assignment 2 |

Assignment 2 Solutions | Assignment 2 Solutions |

Assignment 3 | Assignment 3 |

Assignment 3 Solutions | Assignment 3 Solutions |

Assignment 4 | Assignment 4 |

Assignment 4 Solutions | Assignment 4 Solutions |

Assignment 5 | Assignment 5 |

Assignment 5 Solutions | Assignment 5 Solutions |

Assignment 6 | Assignment 6 |

Assignment 6 Solutions | Assignment 6 Solutions |

Assignment 7 | Assignment 7 |

Assignment 7 Solutions | Assignment 7 Solutions |

Assignment 8 | Assignment 8 |

Assignment 8 Solutions | Assignment 8 Solutions |

Sl.No | Chapter Name | MP4 Download |
---|---|---|

1 | Lec1-Part I-Classification of optimization problems and the place of Calculus of Variations in it | Download |

2 | Lec2-Part II-Classification of optimization problems and the place of Calculus of Variations in it | Download |

3 | Lec3-Part I - Genesis of Calculus of Variations | Download |

4 | Lec4-Part II - Genesis of Calculus of Variations | Download |

5 | Lec5-Part I - Formulation of Calculus of Variations problems in geometry and mechanics and design | Download |

6 | Lec6-Part II - Formulation of Calculus of Variations problems in geometry and mechanics and design | Download |

7 | Lec7-Part I - Unconstrained minimization in one and many variables | Download |

8 | Lec8-Part II - Unconstrained minimization in one and many variables | Download |

9 | Lec9-Part I - Constrained minimization KKT conditions | Download |

10 | Lec10-Part II - Constrained minimization KKT conditions | Download |

11 | Lec11-Part I - Sufficient conditions for constrained minimization | Download |

12 | Lec12-Part II - Sufficient conditions for constrained minimization | Download |

13 | Lec13-Part I-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces | Download |

14 | Lec14-Part II-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces | Download |

15 | Lec15-Function spaces and Gateaux variation | Download |

16 | Lec16-First variation of a functional Freche?t differential and variational derivative | Download |

17 | Lec17-Part I-Fundamental lemma of calculus of variations and Euler Lagrange equations | Download |

18 | Lec18-Part II-Fundamental lemma of calculus of variations and Euler Lagrange equations | Download |

19 | Lec19-Extension of Euler-Lagrange equations to multiple derivatives | Download |

20 | Lec20-Extension of Euler-Lagrange equations to multiple functions in a functional | Download |

21 | Lec 21-Part I-Global Constraints in calculus of variations | Download |

22 | Lec22-Part II-Global Constraints in calculus of variations | Download |

23 | Lec23-Part I-Local (finite subsidiary) constrains in calculus of variations | Download |

24 | Lec 24-Part II-Local (finite subsidiary) constrains in calculus of variations | Download |

25 | Lec25-Part I-Size optimization of a bar for maximum stiffness for given volume | Download |

26 | Lec26-Part II-Size optimization of a bar for maximum stiffness for given volume | Download |

27 | Lec27-Part III-Size optimization of a bar for maximum stiffness for given volume | Download |

28 | Lec28-Part I-Calculus of variations in functionals involving two and three independent variables | Download |

29 | Lec29-Part II-Calculus of variations in functionals involving two and three independent variables | Download |

30 | Lec30-Part I-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions | Download |

31 | Lec31-Part II-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions | Download |

32 | Lec32-Variational (energy) methods in statics; principles of minimum potential energy and virtual work | Download |

33 | Lec33-Part I-General framework of optimal structural designs | Download |

34 | Lec34-Part II-General framework of optimal structural designs | Download |

35 | Lec35-Optimal structural design of bars and beams using the optimality criteria method | Download |

36 | Lec36-Invariants of Euler-Lagrange equations and canonical forms | Download |

37 | Lec37-Noether’s theorem | Download |

38 | Lec38-Minimum characterization of Sturm-Liouville problems | Download |

39 | Lec39-Rayleigh quotient for natural frequencies and mode shapes of elastic systems | Download |

40 | Lec40-Stability analysis and buckling using calculus of variations | Download |

41 | Lec41-Strongest (most stable) column | Download |

42 | Lec42-Dynamic compliance optimization | Download |

43 | Lec43-Electro-thermal-elastic structural optimization | Download |

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 | Download |

Sl.No | Chapter Name | English |
---|---|---|

1 | Lec1-Part I-Classification of optimization problems and the place of Calculus of Variations in it | PDF unavailable |

2 | Lec2-Part II-Classification of optimization problems and the place of Calculus of Variations in it | Download Verified |

3 | Lec3-Part I - Genesis of Calculus of Variations | Download Verified |

4 | Lec4-Part II - Genesis of Calculus of Variations | Download Verified |

5 | Lec5-Part I - Formulation of Calculus of Variations problems in geometry and mechanics and design | Download Verified |

6 | Lec6-Part II - Formulation of Calculus of Variations problems in geometry and mechanics and design | Download Verified |

7 | Lec7-Part I - Unconstrained minimization in one and many variables | Download Verified |

8 | Lec8-Part II - Unconstrained minimization in one and many variables | Download Verified |

9 | Lec9-Part I - Constrained minimization KKT conditions | Download Verified |

10 | Lec10-Part II - Constrained minimization KKT conditions | Download Verified |

11 | Lec11-Part I - Sufficient conditions for constrained minimization | Download Verified |

12 | Lec12-Part II - Sufficient conditions for constrained minimization | Download Verified |

13 | Lec13-Part I-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces | Download Verified |

14 | Lec14-Part II-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces | Download Verified |

15 | Lec15-Function spaces and Gateaux variation | Download Verified |

16 | Lec16-First variation of a functional Freche?t differential and variational derivative | Download Verified |

17 | Lec17-Part I-Fundamental lemma of calculus of variations and Euler Lagrange equations | Download Verified |

18 | Lec18-Part II-Fundamental lemma of calculus of variations and Euler Lagrange equations | Download Verified |

19 | Lec19-Extension of Euler-Lagrange equations to multiple derivatives | Download Verified |

20 | Lec20-Extension of Euler-Lagrange equations to multiple functions in a functional | Download Verified |

21 | Lec 21-Part I-Global Constraints in calculus of variations | PDF unavailable |

22 | Lec22-Part II-Global Constraints in calculus of variations | PDF unavailable |

23 | Lec23-Part I-Local (finite subsidiary) constrains in calculus of variations | PDF unavailable |

24 | Lec 24-Part II-Local (finite subsidiary) constrains in calculus of variations | PDF unavailable |

25 | Lec25-Part I-Size optimization of a bar for maximum stiffness for given volume | PDF unavailable |

26 | Lec26-Part II-Size optimization of a bar for maximum stiffness for given volume | PDF unavailable |

27 | Lec27-Part III-Size optimization of a bar for maximum stiffness for given volume | PDF unavailable |

28 | Lec28-Part I-Calculus of variations in functionals involving two and three independent variables | PDF unavailable |

29 | Lec29-Part II-Calculus of variations in functionals involving two and three independent variables | PDF unavailable |

30 | Lec30-Part I-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions | PDF unavailable |

31 | Lec31-Part II-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions | PDF unavailable |

32 | Lec32-Variational (energy) methods in statics; principles of minimum potential energy and virtual work | PDF unavailable |

33 | Lec33-Part I-General framework of optimal structural designs | PDF unavailable |

34 | Lec34-Part II-General framework of optimal structural designs | PDF unavailable |

35 | Lec35-Optimal structural design of bars and beams using the optimality criteria method | PDF unavailable |

36 | Lec36-Invariants of Euler-Lagrange equations and canonical forms | PDF unavailable |

37 | Lec37-Noether’s theorem | PDF unavailable |

38 | Lec38-Minimum characterization of Sturm-Liouville problems | PDF unavailable |

39 | Lec39-Rayleigh quotient for natural frequencies and mode shapes of elastic systems | PDF unavailable |

40 | Lec40-Stability analysis and buckling using calculus of variations | PDF unavailable |

41 | Lec41-Strongest (most stable) column | PDF unavailable |

42 | Lec42-Dynamic compliance optimization | PDF unavailable |

43 | Lec43-Electro-thermal-elastic structural optimization | PDF unavailable |

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 | PDF unavailable |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |