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

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2 One-dimensional applications: A = difference matrix

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3 Network applications: A = incidence matrix

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4 Applications to linear estimation: least squares

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5 Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F(t)

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6 Underlying theory: applied linear algebra

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7 Discrete vs. continuous: differences and derivatives

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8 Applications to boundary value problems: Laplace equation

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9 Solutions of Laplace equation: complex variables

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10 Delta function and Green's function

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11 Initial value problems: wave equation and heat equation

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12 Solutions of initial value problems: eigenfunctions

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13 Numerical linear algebra: orthogonalization and A = QR

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14 Numerical linear algebra: SVD and applications

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15 Numerical methods in estimation: recursive least squares and covariance matrix

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16 Dynamic estimation: Kalman filter and square root filter

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17 Finite difference methods: equilibrium problems

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18 Finite difference methods: stability and convergence

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19 Optimization and minimum principles: Euler equation

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20 Finite element method: equilibrium equations

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21 Spectral method: dynamic equations

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22 Fourier expansions and convolution

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23 Fast fourier transform and circulant matrices

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24 Discrete filters: lowpass and highpass

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25 Filters in the time and frequency domain

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26 Filter banks and perfect reconstruction

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27 Multiresolution, wavelet transform and scaling function

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28 Splines and orthogonal wavelets: Daubechies construction

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29 Applications in signal and image processing: compression

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30 Network flows and combinatorics: max flow = min cut

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31 Simplex method in linear programming

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32 Nonlinear optimization: algorithms and theory

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