| LEC # | TOPICS | VIDEOS |
|---|---|---|
| 1 | Positive definite matrices K = A'CA | (56K) (220K) |
| 2 | One-dimensional applications: A = difference matrix | (56K) (220K) |
| 3 | Network applications: A = incidence matrix | (56K) (220K) |
| 4 | Applications to linear estimation: least squares | (56K) (220K) |
| 5 | Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F(t) | (56K) (220K) |
| 6 | Underlying theory: applied linear algebra | (56K) (220K) |
| 7 | Discrete vs. continuous: differences and derivatives | (56K) (220K) |
| 8 | Applications to boundary value problems: Laplace equation | (56K) (220K) |
| 9 | Solutions of Laplace equation: complex variables | (56K) (220K) |
| 10 | Delta function and Green's function | (56K) (220K) |
| 11 | Initial value problems: wave equation and heat equation | (56K) (220K) |
| 12 | Solutions of initial value problems: eigenfunctions | (56K) (220K) |
| 13 | Numerical linear algebra: orthogonalization and A = QR | (56K) (220K) |
| 14 | Numerical linear algebra: SVD and applications | (56K) (220K) |
| 15 | Numerical methods in estimation: recursive least squares and covariance matrix | (56K) (220K) |
| 16 | Dynamic estimation: Kalman filter and square root filter | (56K) (220K) |
| 17 | Finite difference methods: equilibrium problems | (56K) (220K) |
| 18 | Finite difference methods: stability and convergence | (56K) (220K) |
| 19 | Optimization and minimum principles: Euler equation | (56K) (220K) |
| 20 | Finite element method: equilibrium equations | (56K) (220K) |
| 21 | Spectral method: dynamic equations | (56K) (220K) |
| 22 | Fourier expansions and convolution | (56K) (220K) |
| 23 | Fast fourier transform and circulant matrices | (56K) (220K) |
| 24 | Discrete filters: lowpass and highpass | (56K) (220K) |
| 25 | Filters in the time and frequency domain | (56K) (220K) |
| 26 | Filter banks and perfect reconstruction | (56K) (220K) |
| 27 | Multiresolution, wavelet transform and scaling function | (56K) (220K) |
| 28 | Splines and orthogonal wavelets: Daubechies construction | (56K) (220K) |
| 29 | Applications in signal and image processing: compression | (56K) (220K) |
| 30 | Network flows and combinatorics: max flow = min cut | (56K) (220K) |
| 31 | Simplex method in linear programming | (56K) (220K) |
| 32 | Nonlinear optimization: algorithms and theory | (56K) (220K) |