Computational Science and Engineering I

MIT , Prof.Gilbert Strang

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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