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Lecture
Two-Stream Instability: Kinetic Calculation
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Signal Representation: Fourier Transforms
Covers the representation of signals using Fourier transforms and the properties of signal vectors.
Linearization and Dispersion
Covers linearization and Fourier mode analysis techniques applied to Maxwell and two-fluid equations.
Fourier Transform: Concepts and Applications
Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.
Space Trusses & Frames
Covers space trusses, frames, and machines, emphasizing equilibrium analysis and structural design principles.
Two-Fluid Waves
Explores two-fluid waves in plasma physics, discussing dispersion relations and wave propagation characteristics.
Trigonometric Polynomials: Periodicity and Fourier Coefficients
Explores trigonometric polynomials, periodicity, and Fourier coefficients in mathematical analysis.
Distributions and Derivatives
Covers distributions, derivatives, convergence, and continuity criteria in function spaces.
Representation Theory: Algebras and Homomorphisms
Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.
Normed Spaces
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.