Lectures related to Differential Relations for Internal Forces

Buckling of Beams: Moment-Curvature Relation

Explores beam buckling, moment-curvature relation, deflection, and fundamental beam solutions in structural mechanics.

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

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.

Finite Difference Method: Approximating Derivatives and Equations

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

Quantum Mechanics: Power Series Solutions

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

Boundary Conditions and Basis Decomposition

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

Numerical Methods: Boundary Value Problems

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

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Non-Straight Beams in Structural Mechanics

Covers non-straight beams, frames, and matching conditions in structural mechanics.

Numerical Methods for Boundary Value Problems

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

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.

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.

Internal Heat Transfer Effects

Covers internal heat transfer effects in heterogeneous reactions, emphasizing dimensionless numbers and transport effects.

Vibratory Mechanics: Continuous Systems

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

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.

Beam Bending and Buckling

Covers beam bending and buckling, including moment-curvature relationship and deflection of beams.

Climate Modeling: Equations, Numerical Solutions, and Uncertainties

Explores the equations and numerical solutions in climate modeling, highlighting uncertainties in climate projections.

Finite element methods

Covers finite element methods for solving diffusion problems in porous media, including meshing, interpolation, and weighted residuals.

Computational Geomechanics: Week 4

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