Tue-Thu-Sat 9am - MR4

- Lecture 1: Poisson's equation, finite differences, and the five-point formula
- Lecture 2: Five-point formula (continued)
- Lecture 3: Convergence + Fast Poisson solver
- Lecture 4: Fast Fourier Transform + Diffusion equation
- Lecture 5: Stability
- Lecture 6: Stability (examples)
- Lecture 7: Stability using Fourier analysis
- Lecture 8: Stability using Fourier analysis cont'd: wave equations
- Lecture 9: Diffusion equation in 2D
- Lecture 10: Splitting
- Lecture 11: Spectral methods - Fourier approximation of analytic functions
- Lecture 12: Spectral methods - Fourier series for ODEs and PDEs
- Lecture 13: Spectral methods - Chebyshev expansions
- Lecture 14: Spectral methods - Evolution equations
- Lecture 15: Iterative methods for linear systems - Jacobi and Gauss-Seidel methods
- Lecture 16: Iterative methods for linear systems - Convergence of Jacobi and Gauss-Seidel
- Lecture 17: Iterative methods for linear systems - Multigrid methods
- Lecture 18: Iterative methods for linear systems - Steepest descent
- Lecture 19: Iterative methods for linear systems - Conjugate gradient method
- Lecture 20: Iterative methods for linear systems - Convergence of CG
- Lecture 21: Eigenvalues and eigenvectors - Power iteration, inverse iteration, Rayleigh quotient iteration
- Lecture 22: Eigenvalues and eigenvectors - Simultaneous and QR iteration
- Lecture 23: Eigenvalues and eigenvectors - QR iteration: shifts, and deflation
- Lecture 24: Eigenvalues and eigenvectors - Reduction to tridiagonal form, nonsymmetric matrices

The notes are heavily inspired by previous editions of the course, taught by Prof. Anders Hansen and Prof. Arieh Iserles (http://www.damtp.cam.ac.uk/research/afha/lectures/Part_II_NumAn/).

- IB Numerical Analysis course
- Matlab demos
- A first course in the numerical analysis of differential equations, A. Iserles, Cambridge University Press [The course mostly follows this book]
- Iterative methods for sparse linear systems, Y. Saad
- A multigrid tutorial, W. L. Briggs, V. E. Henson, S. F. McCormick
- The definition of numerical analysis by L. N. Trefethen
- Top ten algorithms of the 20th century, by Barry Cipra