Entry requirements

Scientific computing I.

Aims

To give deeper and extended knowledge and skills

about basic concepts in scientific computing and in

numerical methods for important computational

problems in engineering and natural sciences.

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.

Included in the course is also a small project where some the course sections above is used within an application area such as biological systems.

Instruction

Lectures, lessons, laboratory work and compulsory

assignments.

Assessment

Written examination at the end of the course. Compulsory assignments must be passed.