Prerequisite/Recommended prerequisite for participation in the module

The module builds on knowledge obtained by the modules Linear Algebra with Applications, Analysis 1, and Probability Theory from the BSc in Mathematics or similar.

Content, progress and pedagogy of the module

Learning objectives

Knowledge

• have knowledge of floating point arithmetic, including the international standards for floating point arithmetic
• have knowledge of error analysis and stability of numerical algorithms
• have knowledge of polynomial interpolation and its application to the derivation of numerical algorithms
• have knowledge of basic results in approximation theory
• have knowledge of methods for finding zeroes of functions
• have knowledge of numerical linear algebra, in particular algorithms adapted to large sparse systems of linear equations
• have knowledge of methods for numerical differentiation, including spectral methods
• have knowledge of methods for numerical integration, including Gaussian quadrature
• have knowledge of numerical solution methods for ordinary differential equations, including spectral methods
• have knowledge of some probabilistic methods in numerical analysis, including Monte-Carlo methods

Skills

• can implement basic numerical algorithms in different computer architectures
• can choose appropriate numerical methods to solve a given class of problems

Competences

• can evaluate the appropriateness of a given numerical method for solving a class of problems
• are aware of the limitations of numerical methods to solve a class of problems

Extent and expected workload

This is a 5 ECTS project module and the work load is expected to be 150 hours for the student.

Exam

Exams

Name of exam	Numerical Analysis
Type of exam	Oral exam In order to participate in the exam, students must have actively participated in course progress by way of one or several independent oral and/or written contributions.
ECTS	5
Assessment	Passed/Not Passed
Type of grading	Internal examination
Criteria of assessment	As stated in the Joint Programme Regulations. http:/​/​www.engineering.aau.dk/​uddannelse/​Studieadministration/​