# Video Lectures

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™.

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) |