Tue-Thu-Sat 10am - MR4

- Lecture 1: Poisson's equation, finite differences, and the five-point formula
- Lecture 2: Five-point formula (continued)
- Lecture 3: Convergence
- Lecture 4: FFT for Fast Poisson solver + Diffusion equation
- Lecture 5: Stability
- Lecture 6: Crank-Nicolson
- Lecture 7: Stability using Fourier analysis
- Lecture 8: The advection equation
- Lecture 9: The diffusion equation in two space dimensions
- Lecture 10: Splitting schemes
- Lecture 11: Spectral methods (1) - Fourier approximation
- Lecture 12: Spectral methods (2)
- Lecture 13: Spectral methods (3) - Chebyshev approximation
- Lecture 14: Spectral methods (4) - Equations of evolution
- Lecture 15: Iterative methods for linear systems - Jacobi, Gauss-Seidel
- Lecture 16: Iterative methods for linear systems - convergence, relaxation
- 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
- Lecture 20: Iterative methods for linear systems - CG convergence and preconditioning
- 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 and slides are heavily inspired by last year's edition of the course, taught by Prof. Anders Hansen (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