Lectures related to Introduction to Partial Differential Equations

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

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

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

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

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

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

Covers the heat equation, its physical interpretation, and numerical methods for solving it.

Explores the parabolic heat equation evolution and numerical solution methods.

Covers the fundamentals of heat transfer, including radiative properties, boundary layer theory, and Prandtl number.

Covers the fundamentals of two-phase flow and heat transfer phenomena.

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

Explores the basics of heat conduction in solids, covering Fourier's law, thermal conductivity, energy conservation, and practical applications.

Explores the applications of the Fourier equation in heat transfer phenomena.

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

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

Explores heat transfer in windows and coatings, emphasizing reflection minimization and absorption optimization.

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

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Explores internal flows, boundary layers, heat transfer coefficients, and Nusselt number correlations in thermal systems.

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.