# 2019/2020

## Prerequisite/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

Lectures and exercises. Teaching is in English and/or Danish depending on the participation of international students, or if the supervisor is of foreign origin.

Since it is a 5 ECTS course, the work load is expected to be 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