Lectures related to Fermat's principle

Electromagnetic Waves and Optics

Covers the fundamentals of electromagnetic waves and optics, including interference phenomena, diffraction, refraction, and reflection of light.

Hamiltonian Formalism: Harmonic Oscillator

Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.

Hypothesis Testing

Covers hypothesis testing, Neyman-Pearson lemma, ROC curves, and optimal tests with examples and simulations.

Quantum Instanton Theory

Explores quantum instanton theory, path integrals, reaction rates, and tunnelling phenomena.

Introduction to Field Theory

Introduces field theory, focusing on density, springs, canonical transformations, and the principle of least action.

Principle of Least Action

Covers the principle of least action in mechanics and stress forces application.

Derivation of Boundary Conditions

Covers the derivation of boundary conditions for total energy in bending and stretching of plates.

Dynamical Systems: Mathematical Modeling

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

General Physics: Quantum - Image Formation and Geometrical Optics

Explores image formation, optics laws, wavefronts, and mirror reflections in physics.

Symmetry and Conservation Laws

Explores symmetry, Noether's theorem, and conservation laws in physics, emphasizing the role of time and the Hamiltonian.

Algebraic Topology and Differential Geometry

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Geodesics and Surface Area

Explores geodesics as locally shortest paths and defines surface area using parametric squares.

Optical Fiber Sheath: Advantages and Principles

Explores the benefits of sheathing optical fibers and fundamental wave propagation principles.

Derivation of Boundary Conditions in Mechanics of Slender Structures

Covers the derivation of boundary conditions in mechanics of slender structures, focusing on total energy variation and equilibrium equations.

Analytical Mechanics: Equilibrium Positions and Least Action Principle

Explores equilibrium positions, lineic density, and the principle of least action in analytical mechanics.

Principle of Least Action

Explores the principle of least action in mathematics and its application to functional branches.

Euler-Lagrange Equations

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.

Field Theory: Action Principles

Discusses the application of action principles in classical field theory, focusing on Lagrange and Hamiltonian formulations.

Hamilton's Formalism: Equations and Transformations

Explores Hamilton's formalism, canonical equations, and Poisson brackets in classical and quantum mechanics.

Superposition and Interference in Electromagnetic Waves

Explores the superposition and interference of electromagnetic waves, discussing energy redistribution and standing waves.