Entry requirements

Fourier methods. Numerical analysis I.

Aims

To give deeper and extended knowledge and skills

about basic concepts in numerical analysis 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,

Gershgorin circles, Rayleigh quotient, Jocobis

method, the QR method, invers iteration, condition.

Least squares problem: orthogonal polynomials,

QR factorisation. Fourier expansion, the fast

Fourier transform (FFT), overdetermined systems.

Galerkin and Collocation methods for ordinary

differential equations (ODE). Splines. Numerical

solutions to timedependent partial differential

equations (PDE): well posedness, difference schemes,

consistency, stability and convergence. Semidiscrete

methods. Numerical solution to elliptic PDE:s.

Finite element methods. 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.