| Overview of Optimization Calculus of Vibrations |
| Lecture 01 - Classification of Optimization Problems and the Place of Calculus of Variations in it |
| Lecture 02 - Classification of Optimization Problems and the Place of Calculus of Variations in it (cont.) |
| Lecture 03 - Genesis of Calculus of Variations |
| Lecture 04 - Genesis of Calculus of Variations (cont.) |
| Lecture 05 - Formulation of Calculus of Variations Problems in Geometry and Mechanics |
| Lecture 06 - Formulation of Calculus of Variations Problems in Geometry and Mechanics (cont.) |
| Summary of Finite Variable Optimization |
| Lecture 07 - Unconstrained Minimization in One and Many Variables |
| Lecture 08 - Unconstrained Minimization in One and Many Variables (cont.) |
| Lecture 09 - Constrained Minimization KKT Conditions |
| Lecture 10 - Constrained Minimization KKT Conditions (cont.) |
| Lecture 11 - Sufficient Conditions for Constrained Minimization |
| Lecture 12 - Sufficient Conditions for Constrained Minimization (cont.) |
| Mathematical Preliminaries for Calculus of Variations |
| Lecture 13 - Function and Functional, Metrics and Metric Space, Norm and Vector Spaces |
| Lecture 14 - Function and Functional, Metrics and Metric Space, Norm and Vector Spaces (cont.) |
| Lecture 15 - Function Spaces and Gateaux Variation |
| Lecture 16 - First Variation of a Functional Frechet Differential and Variational Derivative |
| Lecture 17 - Fundamental Lemma of Calculus of Variations and Euler-Lagrange Equation |
| Lecture 18 - Fundamental Lemma of Calculus of Variations and Euler-Lagrange Equation (cont.) |
| Euler-Lagrange Equation with and without Constraints |
| Lecture 19 - Extension of Euler-Lagrange Equation to Multiple Derivatives |
| Lecture 20 - Extension of Euler-Lagrange Equation to Multiple Functions in a Functional |
| Lecture 21 - Global Constraints in Calculus of Variations |
| Lecture 22 - Global Constraints in Calculus of Variations (cont.) |
| Lecture 23 - Local (Finite Subsidiary) Constraints in Calculus of Variations |
| Lecture 24 - Local (Finite Subsidiary) Constraints in Calculus of Variations (cont.) |
| Size Optimization of a Bar for Maximum Stiffness for Given Volume |
| Lecture 25 - Size Optimization of a Bar for Maximum Stiffness for Given Volume I |
| Lecture 26 - Size Optimization of a Bar for Maximum Stiffness for Given Volume II |
| Lecture 27 - Size Optimization of a Bar for Maximum Stiffness for Given Volume III |
| Lecture 28 - Calculus of Variations in Functionals involving Two and Three Independent Variables |
| Lecture 29 - Calculus of Variations in Functionals involving Two and Three Independent Variables (cont.) |
| Advanced Concepts and General Framework for Optimal Structural Design |
| Lecture 30 - General Variation of a Functional, Transversality Conditions; Broken Examples, Weierstrass-Erdmann Corner Conditions |
| Lecture 31 - General Variation of a Functional, Transversality Conditions; Broken Examples, Weierstrass-Erdmann Corner Conditions (cont.) |
| Lecture 32 - Variational (Energy) Methods in Statics; Principles of Minimum Potential Energy and Virtual Work |
| Lecture 33 - General Framework of Optimal Structural Designs |
| Lecture 34 - General Framework of Optimal Structural Designs (cont.) |
| Lecture 35 - Optimal Structural Design of Bars and Beams using the Optimality Criteria Method |
| First Integrals, Invariants, and Noether's Theorem and Minimum Characterization of Eigenvalue Problems |
| Lecture 36 - Invariants of Euler-Lagrange Equation and Canonical Forms |
| Lecture 37 - Noether's Theorem |
| Lecture 38 - Minimum Characterization of Sturm-Liouville Problems |
| Lecture 39 - Rayleigh Quotient for Natural Frequencies and Mode Shapes of Elastic Systems |
| Lecture 40 - Stability Analysis and Buckling using Calculus of Variations |
| Optimal Structural Design and Inverse of Euler-Lagrange Equation |
| Lecture 41 - Strongest (Most Stable) Column |
| Lecture 42 - Dynamic Compliance Optimization |
| Lecture 43 - Electro-thermal-elastic Structural Optimization |
| Lecture 44 - Formulating the Extremization Problem |