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Linear Algebra

By Gilbert Strang – MIT


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

Artificial Intelligence

By Sebastian Thrun & Peter Norvig – Stanford

Machine Learning

By Andrew Ng – Stanford

Other great resources