Unbounded and Bounded Systems: Fourier Methods

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Explores the motivation behind Fourier series and transforms, their fundamentals, and applications in solving differential equations.

Explores the Fourier Trick for time-dependent diffusion problems in a Cartesian system.

Explores the applications of the Fourier equation in heat transfer phenomena, covering conduction, convection, and radiation.

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

Covers Fourier series, periodic functions, and Fourier transforms.

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

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

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

Explores Fourier series, DFT, FFT, and their applications in signal processing and spectroscopy.

Explores filter design, boundary conditions, Fourier-domain filtering, and useful smoothing filters for image processing.