MA5233 Computational Mathematics     
 

Mondays 7:00-10:00 pm, S14-06SR



Syllabus

Lectures
  •  Lecture 1 (13 August): Review of linear algebra; orthogonal vectors and matrices, norms, the singaular value decomposition (SVD), projectors.
  •  Lecture 2 (27 August): QR factorization; Gram-Schmidt orthogonalization; Householder triangularization; conditioning and condition numbers; backward error analysis.
  •  Lecture 3 (3 September): Gaussian elimination; pivoting; stability of Gaussian elimination; Cholesky factorization.
  •  Lecture 4 (10 September) : The Arnoldi iteration and GMRES.
  •  Lecture 5 (17 September) : The conjugate gradient method. Matlab code: CG.m
  •  Lecture 6 (1 October) : Eigenvalue problems for real symmetric matrices. reduction to tridiagonal form; Rayleigh quotient and inverse iteration; QR algorithm.
  •  Lecture 7 (8 October): Introduction to numerical ODE; Consistency, 0-stability, convergence; forward and backward Euler methods; Runge-Kutta method
  •  Lecture 8 (15 October): Runge-Kutta method; multi-step methods, order condition, root condition
  •  Lecture 9 (22 October): BDF; finite difference methods for Laplace/Possion equation.
  •  Lecture 10 (5 November): finite difference methods for diffusion equation; Von Neumann stability analysis.

Assignments
   
Assignment 1 - due 10 September 2012
Assignment 2 - due 21 September 2012
Assignment 3 - due 8 October 2012
Assignment 4 - due 22 October 2012
Assignment 5 - due 5 November 2012
Assignment 6 - due 16 November 2012