SF1546 Numerical Methods, Basic Course

Active participation in SF1625 Calculus in one variable or SF1673 Analysis in one variable.

Active participation in DD1310 Programming Techniques or DD1312 Programming Techniques and Matlab or DD1316 Programming Techniques and C.

Basic ideas and concepts: algorithm, local linearisation, iteration, extrapolation, discretisation, convergence, stability, condition.

Estimation of reliability: parameter sensitivity, experimental perturbation calculation, precision.

Numerical methods for: linear systems of equations, nonlinear equations and systems of equations, interpolation, model adaptation with the least squares method, optimisation, integrals and differential equations.

Using mathematical software to solve engineering mathematical problems, make numerical experiments and present solutions.

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.