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Computational Science and Engineering I

Lecture 41: Discrete Fourier series

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Course Description :

Four special matrices - Key ideas of linear algebra - Difference equations - Solving a linear system - Delta function day - Eigenvalues - Positive definite day - Springs and masses; the main framework - Oscillation - Finite differences in time; least squares - Graphs and networks - Kirchhoffs Current Law - Exam Review - Trusses and AsupT CA - Finite elements in 1D - Quadratic/cubic elements - Element matrices; 4th order bending equations - Boundary conditions, splines, gradient and divergence - Gradient and divergence - Laplace equation - Fast Poisson solver - Finite elements in 2D - Fourier series - Discrete Fourier series - Examples of discrete Fourier transform; fast Fourier transform - convolution - filtering - Filters; Fourier integral transform - Convolution equations: deconvolution; convolution in 2D - Sampling Theorem

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