Entry requirements

Transform methods or Fourier methods. 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, orthogonalisation, the QR method, invers iteration.

Least squares problem: orthogonal polynomials,

QR factorisation, overdetermined systems. Discrete Fourier transform, the fast Fourier transform (FFT). 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. Compulsory assignments must be passed.