# 2018/2019

## Prerequisite/Recommended prerequisite for participation in the module

Linear Algebra and Calculus

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

Students who have passed the module should be able to

• Account for basic modeling and analysis of certain ordinary and partial differential equations
• Account for basic analysis of the above ordinary and partial differential equations
• Account for basic concepts of numerical methods
• Explain numerically solving non-linear systems of equations, integrals, and ordinary and partial differential equations
• Account for the modeling and analysis of the above ordinary and partial differential equations

#### Skills

• Use extra- and interpolation techniques such as Taylor polynomials and Lagrange polynomials
• Use Laplace transforms to solve differential equations
• Apply vector analysis and integral principles for mathematical modeling
• Apply methods, analytical as well as numerical, to solve the above ordinary and partial differential equations
• Set up and use the correct numerical method for solving a variety of areas, such as finding the zero point, integration, interpolation, differential equations
• Set up and solve 1- and 2-dimensional heat equations by analytical and numerical methods
• Set up and solve 1- and 2-dimensional wave equations by analytical and numerical methods
• Set up and solve Poisson's and Laplace's equations by numerical methods
• Develop solutions of differential equations using systems of eigenfunctions
• Solve partial differential equations using Fourier series and the separation method

#### Competences

• Engage in a dialogue regarding the optimal choice of analytical and numerical solution methods for partial differential equations, and results from mathematical modeling in general
• Disseminate setup and results of solving certain partial differential equations to others, including colleagues, government agencies and others

### Type of instruction

• Lectures and theoretical exercises

150 hours

## Exam

### Exams

 Name of exam Mathematical Modeling and Numerical Methods Type of exam Written or oral exam ECTS 5 Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment As stated in the Joint Programme Regulations