Lectures related to Laplacian: Basics and Examples

Covers the heat equation for diffusion and conservation of thermal energy.

Covers the analysis of scalar fields, including divergence, gradient, and Laplacian.

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

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Covers the application of separation of variables method to solve the heat equation.

Introduces differential operators, gradient, and divergence in vector fields.

Covers vector fields, gradient, divergence, heat flux, and stress tensors.

Explores the maximum principle in the context of the heat equation and the concept of the cylinder.

Covers the magnetic thickness, short and long junctions, and critical current.