Lectures related to Wave Equations: Vibrating String

High Order Methods: Space Discretisation

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

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.

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 Elements: Elasticity and Variational Formulation

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

Numerical Methods for Boundary Value Problems

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

Hyperbolic Problems: Transport Equation

Covers hyperbolic problems and the transport equation, emphasizing the importance of weak solutions and the conservative transport equation.

Elastic Membrane Boundary Problem 2D

Covers the elastic membrane boundary problem in 2D, exploring mathematical formulation and solution methods.

Continuum Mechanics: Conservation Laws, Tensor Objects, and Fluid Dynamics Log in to Mediaspace to watch this video

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

Eigenstate Thermalization Hypothesis Log in to Mediaspace to watch this video

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

Advection-Diffusion Equations Log in to Mediaspace to watch this video

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 Log in to Mediaspace to watch this video

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

Mechanical Energy Conservation Log in to Mediaspace to watch this video

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

Numerical Methods: Euler and Crank-Nicolson Log in to Mediaspace to watch this video

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

Structural Mechanics Principles: Equilibrium and Stability Log in to Mediaspace to watch this video

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

Fundamentals of Electromagnetic Waves and Their Properties Log in to Mediaspace to watch this video

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

Wave Equation Stability Log in to Mediaspace to watch this video

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

Calculus of Variations and Euler's Elastica Log in to Mediaspace to watch this video

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

Finite Differences in Advection-Diffusion Log in to Mediaspace to watch this video

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