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Lecture
Fourier Series: Understanding Coefficients and Periodicity
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Fourier Transform: Properties and Applications
Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.
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Explores the Central Limit Theorem, convergence in law, characteristic functions, and moment problems in probability theory.
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Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.
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Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.
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Covers the Fourier transform in Analysis IV, discussing Fourier series and solutions for various problems.
Convergence of Fourier Series
Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.
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Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.
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Fourier Series and Transforms: Introduction and Properties
Covers Fourier series, Fourier transforms, and convolution properties, including linearity and commutativity.
Fourier Transform: Properties and Convolution
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