Licence:
Course Description:
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Lectures:
Lecture 1 - Positive definite matrices K = A'CA
Lecture 2 - One-dimensional applications: A = difference matrix
Lecture 3 - Network applications: A = incidence matrix
Lecture 4 - Applications to linear estimation: least squares
Lecture 5 - Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F(t)
Lecture 6 - Underlying theory: applied linear algebra
Lecture 7 - Discrete vs. continuous: differences and derivatives
Lecture 8 - Applications to boundary value problems: Laplace equation
Lecture 9 - Solutions of Laplace equation: complex variables
Lecture 10 - Delta function and Green's function
Lecture 11 - Initial value problems: wave equation and heat equation
Lecture 12 - Solutions of initial value problems: eigenfunctions
Lecture 13 - Numerical linear algebra: orthogonalization and A = QR
Lecture 14 - Numerical linear algebra: SVD and applications
Lecture 15 - Numerical methods in estimation: recursive least squares and covariance matrix
Lecture 16 - Dynamic estimation: Kalman filter and square root filter
Lecture 17 - Finite difference methods: equilibrium problems
Lecture 18 - Finite difference methods: stability and convergence
Lecture 19 - Optimization and minimum principles: Euler equation
Lecture 20 - Finite element method: equilibrium equations
Lecture 21 - Spectral method: dynamic equations
Lecture 22 - Fourier expansions and convolution
Lecture 23 - Fast fourier transform and circulant matrices
Lecture 24 - Discrete filters: lowpass and highpass
Lecture 25 - Filters in the time and frequency domain
Lecture 26 - Filter banks and perfect reconstruction
Lecture 27 - Multiresolution, wavelet transform and scaling function
Lecture 28 - Splines and orthogonal wavelets: Daubechies construction
Lecture 29 - Applications in signal and image processing: compression
Lecture 30 - Network flows and combinatorics: max flow = min cut
Lecture 31 - Simplex method in linear programming
Lecture 32 - Nonlinear optimization: algorithms and theory
Source: http://academicearth.org/courses/computational-science-and-engineering-i
