Recommended prerequisite for participation in the module

The module is based on knowledge achieved in the module "Applied engineering mathematics" or similar.

Content, progress and pedagogy of the module

Learning objectives

Knowledge

• Comprehend the solution of partial differential equations with analytical methods.
• Comprehend different numerical methods.
• Comprehend finite difference, finite volume and the Finite Element Method.

Skills

• Be able to use analytical methods for solving partial differential equations, including:
  • Separation Method and D'Alembert's principle
• Be able to apply numerical methods for solving mathematical problems, including:
  • Linear equations
  • Gauss elimination
  • Factorization methods
  • Iterative solution of linear equation systems, including Gauss-Seidel
  • Ill-conditioned linear equation systems
  • Matrix eigenvalue problems
  • Solution of non-linear equations
  • Interpolation
  • Splines
  • Numerical solution of a definite integral
  • Numerical solution of first order differential equations
  • Numerical solution of second order differential equations
• Be able to apply the finite difference method for solving partial differential equations, including:
  • Difference approximations
  • Elliptic equations
  • Dirichlet and Neumann boundary conditions
  • Parabolic equations
  • Explicit and implicit methods
  • Theta method
  • Hyperbolic equations
  • The use of the Finite Volume Method
• Be able to understand the Finite Element Method for the solution of partial differential equations.

Competences

• Be able to handle development-oriented environments involving numerical methods in study or work contexts.
• Be able to independently engage in disciplinary and interdisciplinary collaboration with a professional approach within mathematical numerical methods.
• Be able to identify own learning needs and to structure own learning in numerical methods.

Type of instruction

The teaching is organized in accordance with the general form of teaching. Please see § 17 in the BSc curriculum and §18 in the BE curriculum.

Extent and expected workload

Since it is a 5 ECTS course module the expected workload is 150 hours for the student.

Exam

Exams

Name of exam	Numerical Methods
Type of exam	Oral exam
ECTS	5
Assessment	7-point grading scale
Type of grading	Internal examination
Criteria of assessment	The criteria of assessment are stated in the Examination Policies and Procedures