Lectures related to Wave Equations: Vibrating String

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Continuum Mechanics: Conservation Laws, Tensor Objects, and Fluid Dynamics

Covers conservation laws, tensor objects, and fluid dynamics in Continuum Mechanics.

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Advection-Diffusion Equations

Explores numerical solutions and stability analysis of advection-diffusion equations, emphasizing properties of analytical solutions and their behavior over time.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Mechanical Energy Conservation

Explores mechanical energy conservation, harmonic oscillators, and equilibrium in mechanical systems.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Structural Mechanics Principles: Equilibrium and Stability

Explores the principles of structural mechanics, including internal loads, equilibrium stability, and the superposition principle.

Fundamentals of Electromagnetic Waves and Their Properties

Provides an overview of electromagnetic wave properties, including speed, refraction, frequency spectrum, and polarization.

Wave Equation Stability

Explores the stability of the wave equation finite difference scheme and resonant excitation.

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Central Motion: Trajectories and Energy

Explores central motion properties, energy conservation, and trajectory parameter determination based on mechanical energy and angular momentum.

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.

Introduction to Partial Differential Equations

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Conservation of Mechanical Energy

Explores the conservation of mechanical energy and its application in solving physics problems involving work, stability, and energy transformations.

Finite Differences in Advection-Diffusion

Explores the explicit 2-level scheme for advection-diffusion and the convergence of digital solutions.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.

Numerical Differentiation and Integration

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Elasto-gravitary Bending: Mechanics of Slender Structure

Explores large deformations of inextensible sheets bent under self-weight and their equilibrium shapes under gravity.