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Lecture
Fourier Series: Parseval Identity
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Fourier Series: Complex Case
Covers the calculation of Fourier coefficients for periodic complex signals and the concept of a complete orthonormal system.
Vibration of Diatomic Molecules
Explores the vibration of diatomic AB molecules and Fourier series, emphasizing equations of motion and Dirichlet's theorem.
Fourier Series: Examples
Explores examples of Fourier series coefficients and applications in various functions.
Uniform Convergence of Fourier Series
Covers the concept of uniform convergence of Fourier series and Dirichlet's theorem application.
Spectral Properties of Fourier Series and Fourier Transforms
Explores the motivation behind Fourier series and transforms, their fundamentals, and applications in solving differential equations.
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Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.
Fourier Transforms: Properties and Applications
Explores Fourier transforms, including properties, convolution, Parseval's theorem, and energy spectral density for non-periodic functions.
Unbounded and Bounded Systems: Fourier Methods
Explores the spectral properties of unbounded and bounded systems using Fourier methods and emphasizes the importance of choosing the correct representation for different boundary conditions.