Special software is required to use some of the files in this section: .rm.
These videos of Professor Strang's lectures were recorded at MIT's Lincoln Laboratory in the Spring of 2001. (Note: This course was previously called "Mathematical Methods for Engineers I".)
These files are also available from iTunes® and YouTube™.
Video lectures.
| 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)
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| 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)
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| 7 |
Discrete vs. continuous: differences and derivatives |
(56K)
(220K)
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| 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)
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| 11 |
Initial value problems: wave equation and heat equation |
(56K)
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| 12 |
Solutions of initial value problems: eigenfunctions |
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| 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 |
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(220K)
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