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Harmonic analysis
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Mixture models: nesting structures
Covers mixture models, nesting structures, and identification issues in discrete choice analysis.
Fourier Transform and Schwartz Space
Explores the Fourier transform, Schwartz space, and Riemann-Lebesgue lemma in quantum physics.
DFT example - analysis of musical instruments
Explores the analysis of musical instruments, including pitch, frequency, harmonics, and timbre.
Linearization and Dispersion
Covers linearization and Fourier mode analysis techniques applied to Maxwell and two-fluid equations.
Fourier Analysis: Series and Divergence Theorem
Covers Fourier analysis, series convergence, divergence theorem, and vector analysis.
Lebesgue Measure and Fourier Analysis
Explores Lebesgue measure, Fourier analysis, PDE applications, and optimal transport in PDEs.
Forced Harmonic Oscillator: Resonance Phenomenon
Covers the forced and damped harmonic oscillator, including the harmonic solution and resonance phenomenon.
Fourier Analysis and PDEs
Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.
Signals, Frequencies and Bandwidth
Introduces signals, frequencies, and bandwidth, including pure sinusoids, Fourier theory, and spectral representation.
Fundamental Solutions of Laplace Equation
Covers the fundamental solutions of the Laplace equation and introduces distributions.