Brownian Motion: Fundamentals and Applications

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Fourier Transform and Spectral Densities

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.

Signal Processing Fundamentals

Explores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.

Stochastic Processes: Brownian Motion

Explores Brownian motion, Langevin equations, and stochastic processes in physics.

White Noise Form of the Langevin Equation

Covers the white noise form of the Langevin equation and its applications.

Causal Systems & Transforms: Delay Operator Interpretation

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

Brownian Motion: From Molecules to Cells

Explores the core concepts of Brownian motion, from molecules to cells, including its history, hypothesis versus description, Langevin's solution, and methods for measuring Brownian motion.

Harmonic Signals and Spectrum Estimation

Explores harmonic signals, spectrum estimation, and signal analysis methods using MATLAB tools.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Fokker-Planck Equations

Explores Fokker-Planck equations, escape rates, and first passage time analysis in statistical physics.

Langevin dynamics: Path Integral Methods

Covers Langevin dynamics, Fokker-Planck equation, solving the Langevin equation, and efficiency of Langevin sampling in molecular dynamics.