1. Numerical linear algebra: SVD, Gram-Schmidt, QR decomposition, Householder reflections, Least squares algorithms, steepest descent, conjugate gradients.

2. Fourier analysis: periodic functions, Fourier series, convergence of Fourier series, Fourier transform, bandlimited functions, sampling theorem, discrete Fourier transform, fast Fourier transform.

3. Numerical methods for ODEs: initial value problems, one step methods, Euler's method, Runge-Kutta methods, boundary values problems.