Lectures related to Untitled | EPFL Graph Search

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

Explores the mechanics of a helix under gravity, studying equilibrium shapes and solving differential equations for helix components.

Quantum Mechanics: Power Series Solutions

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Beam Deflection: Integrating Loads to Deformation

Explores integrating loads to deform beams, emphasizing boundary conditions and practical applications in stress analysis.

Inverse Monotonicity: Stability and Convergence

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Vibratory Mechanics: Continuous Systems

Explores vibratory mechanics in continuous systems, covering separation of variables, boundary conditions, and harmonic solutions.

Numerical Groundwater Flow Resolution: Finite Elements

Covers the numerical resolution of groundwater flows using finite elements and emphasizes the importance of spatial and temporal discretization.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Fixed Energy Propagator: Density and Examples

Covers the fixed energy propagator, including its analytic structure and examples of free particle and barrier penetration.

Analysis IV: Laplace Equation Solutions

Explores Laplace equation solutions through separation of variables and general solution writing for complex problems.

Law of Hooke Applications: Spring Problems

Explores the application of the law of Hooke to spring problems and solving equations of motion for block-spring systems.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Separation of Variables: Spatial Problems

Explores the method of separation of variables for solving spatial problems with second-order ODEs, emphasizing the significance of boundary conditions.

Sturm-Liouville Problem: Legendre Equation

Explores the Sturm-Liouville problem linked to the Legendre equation and its significance in physics.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Heterogeneous Reactions: Transport Effects

Explores transport effects in heterogeneous catalysis, including molecular diffusion and Knudsen diffusion in different types of pores.

Ordinary Differential Equations: Non-linear Analysis

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Linear Differential Equations

Explores solving linear differential equations and the principle of superposition with illustrative examples.