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Sl.No Chapter Name MP4 Download
1Lec1-Part I-Classification of optimization problems and the place of Calculus of Variations in itDownload
2Lec2-Part II-Classification of optimization problems and the place of Calculus of Variations in itDownload
3Lec3-Part I - Genesis of Calculus of VariationsDownload
4Lec4-Part II - Genesis of Calculus of VariationsDownload
5Lec5-Part I - Formulation of Calculus of Variations problems in geometry and mechanics and designDownload
6Lec6-Part II - Formulation of Calculus of Variations problems in geometry and mechanics and designDownload
7Lec7-Part I - Unconstrained minimization in one and many variablesDownload
8Lec8-Part II - Unconstrained minimization in one and many variablesDownload
9Lec9-Part I - Constrained minimization KKT conditionsDownload
10Lec10-Part II - Constrained minimization KKT conditionsDownload
11Lec11-Part I - Sufficient conditions for constrained minimizationDownload
12Lec12-Part II - Sufficient conditions for constrained minimizationDownload
13Lec13-Part I-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spacesDownload
14Lec14-Part II-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spacesDownload
15Lec15-Function spaces and Gateaux variationDownload
16Lec16-First variation of a functional Freche?t differential and variational derivativeDownload
17Lec17-Part I-Fundamental lemma of calculus of variations and Euler Lagrange equationsDownload
18Lec18-Part II-Fundamental lemma of calculus of variations and Euler Lagrange equationsDownload
19Lec19-Extension of Euler-Lagrange equations to multiple derivativesDownload
20Lec20-Extension of Euler-Lagrange equations to multiple functions in a functionalDownload
21Lec 21-Part I-Global Constraints in calculus of variationsDownload
22Lec22-Part II-Global Constraints in calculus of variationsDownload
23Lec23-Part I-Local (finite subsidiary) constrains in calculus of variationsDownload
24Lec 24-Part II-Local (finite subsidiary) constrains in calculus of variationsDownload
25Lec25-Part I-Size optimization of a bar for maximum stiffness for given volumeDownload
26Lec26-Part II-Size optimization of a bar for maximum stiffness for given volumeDownload
27Lec27-Part III-Size optimization of a bar for maximum stiffness for given volumeDownload
28Lec28-Part I-Calculus of variations in functionals involving two and three independent variablesDownload
29Lec29-Part II-Calculus of variations in functionals involving two and three independent variablesDownload
30Lec30-Part I-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditionsDownload
31Lec31-Part II-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditionsDownload
32Lec32-Variational (energy) methods in statics; principles of minimum potential energy and virtual workDownload
33Lec33-Part I-General framework of optimal structural designsDownload
34Lec34-Part II-General framework of optimal structural designsDownload
35Lec35-Optimal structural design of bars and beams using the optimality criteria methodDownload
36Lec36-Invariants of Euler-Lagrange equations and canonical formsDownload
37Lec37-Noether’s theoremDownload
38Lec38-Minimum characterization of Sturm-Liouville problemsDownload
39Lec39-Rayleigh quotient for natural frequencies and mode shapes of elastic systemsDownload
40Lec40-Stability analysis and buckling using calculus of variationsDownload
41Lec41-Strongest (most stable) columnDownload
42Lec42-Dynamic compliance optimizationDownload
43Lec43-Electro-thermal-elastic structural optimizationDownload
44Lec44-Formulating the extremization problem starting from the differential equation, self-adjointness of the differential operator, and methods to deal with conservative and dissipative systemDownload

Sl.No Chapter Name English
1Lec1-Part I-Classification of optimization problems and the place of Calculus of Variations in itPDF unavailable
2Lec2-Part II-Classification of optimization problems and the place of Calculus of Variations in itDownload
Verified
3Lec3-Part I - Genesis of Calculus of VariationsDownload
Verified
4Lec4-Part II - Genesis of Calculus of VariationsDownload
Verified
5Lec5-Part I - Formulation of Calculus of Variations problems in geometry and mechanics and designDownload
Verified
6Lec6-Part II - Formulation of Calculus of Variations problems in geometry and mechanics and designDownload
Verified
7Lec7-Part I - Unconstrained minimization in one and many variablesDownload
Verified
8Lec8-Part II - Unconstrained minimization in one and many variablesDownload
Verified
9Lec9-Part I - Constrained minimization KKT conditionsDownload
Verified
10Lec10-Part II - Constrained minimization KKT conditionsDownload
Verified
11Lec11-Part I - Sufficient conditions for constrained minimizationDownload
Verified
12Lec12-Part II - Sufficient conditions for constrained minimizationDownload
Verified
13Lec13-Part I-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spacesDownload
Verified
14Lec14-Part II-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spacesDownload
Verified
15Lec15-Function spaces and Gateaux variationDownload
Verified
16Lec16-First variation of a functional Freche?t differential and variational derivativeDownload
Verified
17Lec17-Part I-Fundamental lemma of calculus of variations and Euler Lagrange equationsDownload
Verified
18Lec18-Part II-Fundamental lemma of calculus of variations and Euler Lagrange equationsDownload
Verified
19Lec19-Extension of Euler-Lagrange equations to multiple derivativesDownload
Verified
20Lec20-Extension of Euler-Lagrange equations to multiple functions in a functionalDownload
Verified
21Lec 21-Part I-Global Constraints in calculus of variationsPDF unavailable
22Lec22-Part II-Global Constraints in calculus of variationsPDF unavailable
23Lec23-Part I-Local (finite subsidiary) constrains in calculus of variationsPDF unavailable
24Lec 24-Part II-Local (finite subsidiary) constrains in calculus of variationsPDF unavailable
25Lec25-Part I-Size optimization of a bar for maximum stiffness for given volumePDF unavailable
26Lec26-Part II-Size optimization of a bar for maximum stiffness for given volumePDF unavailable
27Lec27-Part III-Size optimization of a bar for maximum stiffness for given volumePDF unavailable
28Lec28-Part I-Calculus of variations in functionals involving two and three independent variablesPDF unavailable
29Lec29-Part II-Calculus of variations in functionals involving two and three independent variablesPDF unavailable
30Lec30-Part I-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditionsPDF unavailable
31Lec31-Part II-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditionsPDF unavailable
32Lec32-Variational (energy) methods in statics; principles of minimum potential energy and virtual workPDF unavailable
33Lec33-Part I-General framework of optimal structural designsPDF unavailable
34Lec34-Part II-General framework of optimal structural designsPDF unavailable
35Lec35-Optimal structural design of bars and beams using the optimality criteria methodPDF unavailable
36Lec36-Invariants of Euler-Lagrange equations and canonical formsPDF unavailable
37Lec37-Noether’s theoremPDF unavailable
38Lec38-Minimum characterization of Sturm-Liouville problemsPDF unavailable
39Lec39-Rayleigh quotient for natural frequencies and mode shapes of elastic systemsPDF unavailable
40Lec40-Stability analysis and buckling using calculus of variationsPDF unavailable
41Lec41-Strongest (most stable) columnPDF unavailable
42Lec42-Dynamic compliance optimizationPDF unavailable
43Lec43-Electro-thermal-elastic structural optimizationPDF unavailable
44Lec44-Formulating the extremization problem starting from the differential equation, self-adjointness of the differential operator, and methods to deal with conservative and dissipative systemPDF unavailable


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