Aims

To give deeper and extended knowledge and skills

about basic concepts in scientific computing and in numerical methods for important computational

problems in natural sciences and engineering.

Content

Matrices and matrix algebra: norms, spectral radius,

condition number, transformations, factorisation.

The eigenvalue problem: diagonalisation, triangularisation, Jacobis

method, the QR method, invers iteration, condition.

Least squares problem: orthogonal polynomials,

QR factorisation, overdetermined systems. Fourier expansion, the fast Fourier transform (FFT). Splines. Numerical

solutions to timedependent partial differential

equations (PDE) in one dimension in space: well posedness, difference schemes,

consistency, stability and convergence. Semidiscrete

methods. Numerical solution to elliptic PDE:s in two dimensions. Finite element methods in one dimension in space. Iterative methods for linear systems.

Instruction

Lectures, lessons, laboratory work and compulsory

assignments.

Assessment

Written examination at the end of the course. Passed

labatory course and compulsory assignments are also

required.