First-order partial differential equation

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

Covers the basics of Partial Differential Equations, including well-posedness, operators, and classification of physical PDEs.

Covers the numerical approximation of PDEs, including Poisson and heat equations, transport phenomena, and incompressible limits.

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Explores solving PDEs using eigenmodes decomposition and Fourier series representation of solutions.

Covers the application of numerical methods to solve differential equations using MATLAB.

Covers stress components, tensor transformation, and invariants in continuum mechanics.

Covers topics on relations, sequences, and summations, including lattices, recurrence relations, and sigma notation.

Covers second-order differential equations, focusing on finding particular solutions and the general solution.