Numerical Methods

The course is included in the study programs Applied Physics and Mathematics - master (5-years), Energy, Climate and Environment - master (5-years). It may also be taken independent of study program. This course is also available for inbound exchange students.

This course gives an introduction to basic concepts and issues of numerical computation. The topics treated include: Binary representation and floating point numbers, round-off errors, conditioning, rates of convergence, truncation and discretization errors, best approximation, numerical stability, and complexity analysis. Selected methods will be covered for some of these classes of problems: Linear systems of equations, nonlinear equations, overdetermined linear systems, numerical differentiation and integration, and numerical solution of differential equations.

Applicants from Nordic countries:

Generell studiekompetanse og følgende spesielle opptakskrav: Matematikk R1 og i tillegg enten:

• Matematikk R2

• Fysikk 1 + 2 eller

• Kjemi 1+ 2 eller

• Biologi 1 + 2 eller

• Informasjonsteknologi 1 +2 eller

• Geofag 1 + 2 eller

• Teknologi og forskningslære 1 + 2

Søknadskode 9197 (kravkode REALFA): Enkeltemner i realfag, lavere grad.

After the course the student should:

• Be able to analyze methods for numerical calculations with respect to errors and complexity
• Have mathematical understanding for the methods they apply
• Know the main features in IEEE-standards for binary number representation
• Be able to use iterative methods, like the Jacobi-method for systems of linear equations, and Newtons method for non-linear equations, and be able to describe convergence properties.
• Be able to describe Gaussian elimination and LU factorization, and know QR factorization, and how this is used to find least squares solutions.
• Know the problem of polynomial interpolation, how to solve it, and how to prove unqueness. They should be able to use Chebychev polynomials as tools.
• Use Taylor¿s theorem to find errors of discretization when calculating dericatives and finite difference.
• Know simple methods for numerical calculation of integrals, such as the Trapezoid method and Simpson¿s formula, and general results about global errors, when local errors are known.
• Know the simplest algorithms for stepwise numerical solution of initial value problems for systems of first order differential equations, and know how to reformulate a higher order differential equation to such a system.

Recommended prerequisites

MAT-1020 Linear algebra

If you pass the examination in this course, you will get an reduction in credits (as stated below), if you previously have passed the following courses:

• MA-224 Numerical calculations 10 ects
• FYS-2011 Numerical simulations 10 ects

Language of instruction and examination

Schedule

This course is open to incoming exchange students.

Study Level: Bachelor's

Admission prerequisites:
To take this course, you must first meet the requirements listed in the “Admission requirements” section above.

For details on how to apply for exchange, course selection guidelines, or to contact the Incoming Admissions Team, please visit: Admission for Student Exchange.

Re-sit examination