# Linear Algebra

By Gilbert Strang – MIT

#### COURSE INDEX

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

# Artificial Intelligence

By Sebastian Thrun & Peter Norvig – Stanford

# Machine Learning

By Andrew Ng – Stanford