SF1544 Numerical Methods, Basic Course IV

  Completed course DD1331 Fundamentals of Programming or DD1312 Programming Techniques and Matlab.

Numerical methods for various types of linear systems of equations (full, triangular, banded), the least squares method for inconsistent systems, nonlinear equations (scalar and system), eigenvalue problem, integration, derivation, interpolation and initial and boundary value problems for ODE. Basic technologies for numerical methods, as iteration, linearisation, discretisation and extrapolation, and theoretical concepts as order of accuracy, speed of convergence, complexity, condition and stability.

A general aim with the course is to give the student the understanding that numerical methods and programming techniques are needed to make reliable and efficient simulations of technical and scientific processes based on mathematical models.

• For a general formulation of a technical or scientific problem: be able to identify and classify the mathematical subproblems that need to be solved, and reformulate them to be suitable for numerical treatment.

• Be able to choose, apply and implement numerical methods to produce a solution to a given problem.

• Be able to use concepts in numerical analysis to describe, characterize and analyze numerical methods and estimate the reliability of numerical results.

• Be able to clearly present problem statements, solution approaches and results.