Prerequisite/Recommended prerequisite for participation in the module

Mathematics

Content, progress and pedagogy of the module

Purpose
Not all mathematical and engineering problems are simple enough to solve analytically. The purpose of this course is to provide the students with tools and methodologies to approach those problems that cannot be solved with 'pen and paper', but requires numerical approximations.

Learning objectives

Knowledge

• Must have understanding of how to solve partial differential equations with analytic methods
• Must have understanding of different numerical methods
• Must have an understanding of finite difference, finite volume and finite element method

Skills

• Shall be able to use  analytical methods for solving partial differential equations, in particular the method of Separation of Variables and D’Alembert’s Principle.
• Shall be able to utilize numerical methods to solve mathematical problems, including:
  • Systems of linear equations, Gauss elimination, and factorization-based method.
  • Iterative solution of systems of linear equations, e.g., Gauss-Seidel.
  • Ill-conditioned systems of linear equations.
  • Matrix Eigen value problems.
  • Solving systems of non-linear equations.
  • Interpolation and splines.
  • Numerical solution of definite integrals.
  • Numerical solution of first- and second-order differential equations.
• Must be able to utilize finite difference methods for solution of partial differential equations, including:
  • Approximation by finite differences.
  • Elliptical equations.
  • Dirichlet and Neumann boundary value problems.
  • Parabolic equations.
  • Explicit and implicit method, the Theta-method.
  • Hyperbolic equations.
  • Relationship with finite volume methods.
• Shall have understanding of finite element methods for solving partial differential equations.

Competences

• Shall demonstrate development of his/her knowledge of, understanding of, and ability to make use of, mathematical theories and methods related to solving technical problems using numerical methods.
• Shall be able to identify their own learning requirements and structure their own learning within the context of numerical mathematics.

Type of instruction

The programme is based on a combination of academic, problem-oriented and interdisciplinary approaches and organised based on the following work and evaluation methods that combine skills and reflection: • Lectures • Classroom instruction • Project work • Workshops • Exercises (individually and in groups) • Teacher feedback • Reflection • Portfolio work

Extent and expected workload

Since it is a 5 ECTS course module, the work load is expected to be 150 hours for the student.

Exam

Exams

Name of exam	Numerical Methods
Type of exam	Written or oral examination
ECTS	5
Permitted aids	With certain aids, see list below Unless otherwise stated in the course description in Moodle, it is permitted to bring all kinds of (engineering) aids including books, notes and advanced calculators. If the student brings a computer, it is not permitted to have access to the Internet and the teaching materials from Moodle must therefore be down loaded in advance on the computer. It is emphasized that no form of electronic communication must take place.
Assessment	7-point grading scale
Type of grading	Internal examination
Criteria of assessment	As stated in the Joint Programme Regulations. http:/​/​www.engineering.aau.dk/​uddannelse/​studieadministration/​