Lectures related to Spatial Base Solutions

Vibrating Plate: Stationary Wave Illustration

Covers the illustration of a stationary wave on a vibrating plate and spatial solution formulas with specific boundary conditions.

Square Potential Well

Covers the concept of a square potential well and the search for solutions using trigonometric functions.

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.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Time-dependent Diffusion: Fourier Trick

Explores the Fourier Trick for time-dependent diffusion problems in a Cartesian system.

Heterogeneous Reactions: Transport Effects

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

Mechanics of Kirchhoff Rods II

Explores the mechanics of Kirchhoff rods, focusing on 3D kinematics and twisted solutions.

Quantum Mechanics: Power Series Solutions

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

Boundary Value Problems in 1D

Discusses boundary value problems in 1D and the mathematical principles involved.

Steady Flow through Unsaturated Zone

Covers the steady flow through the unsaturated zone and explores special cases.

Differential Equations: General Solutions and Methods

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

Poisson Problem: Periodic Boundary Conditions

Explores the Poisson problem with periodic boundary conditions and the application of Fourier series in mathematical modeling.

Boundary Conditions - 1D Systems

Covers boundary conditions for heat diffusion in 1D systems.

Thermal Diffusion: Conservation and Fourier Law

Explains conservation of energy and Fourier's law in thermal diffusion.

Solute Transport in Porous Media

Explores solute transport in porous media, covering advection-diffusion equations, boundary conditions, reactions, and numerical modeling in PHREEQC.

Analysis IV: Laplace Equation Solutions

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

Poincaré - Friedrichs: Theorem and Kernel Inequality

Explores the Poincaré - Friedrichs theorem and kernel inequality in constant conditions and boundary uniqueness.

Computational Geomechanics: Week 4

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Diffusion of Neutrons

Covers the solutions of neutron diffusion, including analytical solutions, Laplacian in different geometries, and the physical significance of the diffusion area.

Diffusion on an Infinite Domain: Green's Approach

Covers diffusion on an infinite domain using Green's method and emphasizes finding steady-state solutions and conservation of material.