Lectures related to Calculus of Variations: Introduction

Calculus of Variations: Direct Method

Covers the direct method of the calculus of variations, focusing on the existence of solutions for minimization problems.

3D Linear Elasticity & Beams

Introduces 3D linear elasticity, beams, dimensional analysis, and mechanics of slender structures.

Quantum Chemistry: Perturbation Theory

Covers perturbation theory in quantum chemistry, variational principle, Pauli principle, and separability of operators.

Supervised Learning with kNN: Regression Model

Covers a simple mathematical model for supervised learning with k-nearest neighbors in regression.

Data Reconciliation: Case Study

Discusses correcting errors in measurements through mathematical expressions and optimization techniques.

Calculus of Variations: Ground States in Quantum Mechanics

Covers the Calculus of Variations to find ground states in quantum mechanics by minimizing energy, discussing the Euler Lagrange equation and the Fundamental Theorem of Young Measure Theory.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in calculating complex integrals.

Optimal Control: Hydropower Management

Covers the optimization of hydropower systems and control strategies for maximizing energy production.

Calculus of Variations: Some Topics

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Dynamical Systems: Mathematical Modeling

Covers mathematical modeling of dynamical systems, focusing on electromechanical systems and DC servomotors.

Principle of Least Action

Covers the principle of least action, Euler-Lagrange equations, Lagrange multipliers, and variational calculus.

Calculus Applications: Lengths and Surfaces of Revolution

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Calculus of Variations and Euler's Elastica

Explores variational methods, Euler's Elastica, numerical and analytical methods, and the buckling of slender structures.

Calculus of Variations

Covers topics in Calculus of Variations, including regularity results and implicit function theorems.

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

Extended Josephson Junctions: Modeling and Critical Current

Covers the magnetic thickness, short and long junctions, and critical current.

Perturbation Theory and Variational Principle

Covers perturbation theory, variational principle, and systematic approaches to determining true energy levels.

Variational Calculus and Least Action Principle

Covers the principle of least action and variational calculus in discovering equations of motion.

Physics: Introduction to Dynamics and Energy

Covers one-dimensional and two-dimensional motion, dynamics, and energy with a focus on mathematical modeling and rigorous approach.