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Lecture
Properties of Fourier and inverse Fourier transforms
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Fourier Transforms: Dirac Delta, Fourier Integral, and Transform
Explores the Dirac delta, Fourier integral, and Fourier transform applications in solving PDE problems.
Complex Integration: Fourier Transform Techniques
Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.
Introduction to the Laplace Transform
Covers the Laplace Transform, LTI systems, Fourier Transforms, and properties.
Numerical Methods: Boundary Value Problems
Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.
Spatio-temporal Spectral Analysis
Covers spatio-temporal spectral analysis, dispersion relations, Fourier transforms, and group velocity.
Fourier Series: Understanding Coefficients and Periodicity
Explores Fourier series coefficients, periodicity, and series relations.
Fourier Transform: Analysis IV
Covers the Fourier transform in Analysis IV, discussing Fourier series and solutions for various problems.
Laplace Transform and LTI Systems
Covers Laplace Transform, Fourier Transforms, transfer functions, LTI systems, and Region of Convergence properties.
Fourier Transform: Derivatives and Formulas
Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.
Fourier Transform: Circuit Analysis
Explores the Fourier transform applied to circuit analysis and its properties.
