Lectures related to Linear PDEs of Order 2

Linear Partial Differential Equations

Explores linear partial differential equations, elliptic PDEs, Laplace equation, boundary conditions, and classical solutions.

Elliptic Equations: Linear and Order

Covers general elliptic equations, including Dirichlet problems and boundary conditions.

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Uniqueness Results for Poisson Equation

Explores uniqueness results for the Poisson equation and harmonic functions with different boundary conditions.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Boundary Conditions and Basis Decomposition

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

Green Functions: Theory and Applications

Explores the theory and applications of Green functions in classical electrodynamics, emphasizing the importance of choosing the right function based on boundary conditions.

Classification of PDEs: Linear, Semi-linear, Quasi-linear

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

Groundwater Flow: Laplace Equation and Boundary Conditions

Explores the Laplace equation, harmonic potential, and boundary conditions in groundwater flow, with practical examples.

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.

Biomechanical Tissues: Non-linear Constitutive Laws

Explores ligamentoplasty outcomes, biomechanical analysis, finite element analysis, and tissue characterization through constitutive laws.

Computational Geomechanics: Unconfined Flow

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

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Computational Geomechanics: Unconfined Flow Analysis

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Linear 2nd Order ODEs: Boundary Value Problems

Explores linear 2nd order ODEs as boundary value problems with various types of conditions, ensuring unique solutions.

Laplace Equation in Polar Coordinates

Explores the Laplace equation in polar coordinates and its solution process through separation of variables.

Boundary Conditions in Harmonic Functions

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin conditions.

Rectangular Waveguides: TE and TM Modes

Covers guided propagation in rectangular waveguides for TE and TM modes.

Partial Differential Equations: Viscoelastic Materials

Explores the application of PDEs in viscoelastic materials and materials science.