# 2019/2020

## Prerequisite/Recommended prerequisite for participation in the module

The module builds on knowledge gained in Linear Algebra and Calculus

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

Students who have passed the module

• Must have knowledge about basic modeling of 1. order and second order differential equations.
• Must have knowledge about basic modeling of elliptic, hyperbolic and parabolic partial differential equations.
• Must have knowledge about basic analysis of the above ordinary and partial differential equations
• Must have a basic knowledge about solving 1. order and second order differential equations, including Euler Cauchy-equations.
• Must have knowledge about basic concepts of numerical methods.
• Must have knowledge about numerically solving non-linear equation systems, integrals, and ordinary and partial differential equations
• Must have an understanding about- and be able to use interpolation techniques as, Taylor polynomial, LaGrange polynomial and Newton 's Divided.
• Must have an understanding about- and be able to use Laplace transforms to solve differential equations.
• Must have knowledge about divergence and rotation of vector fields
• Must have an understanding about- and be able to use Gauss' divergence, Stokes - and Greens phrases

#### Skills

• Must demonstrate understanding of the modeling and analysis of the above ordinary and partial differential equations
• Must be able to apply vector analysis and integral principles for mathematical modeling
• Must be able to apply methods, analytical as well as numerical, to solve the above ordinary and partial differential equations
• Must be able toset up and usethe correctnumericalmethodfor solving avariety of areas,such asfinding the zeropoint, integration, interpolation,differential equations.
• Must be able to set up and solve 1. - and 2.-dimensional heat conduction equations by analytical and numerical methods
• Must be able to set up and solve 1. - and 2.-dimensional wave equations by analytical and numerical methods
• Must be able to set up and solve Poisson's and Laplace 's equations by numerical methods
• Must be able to develop solutions of differential equations for the system of eigen functions
• Must be able to solve the above partial differential equations using Fourier series and the separation method
• Must be able to use the Finite Element Method and the Finite Volume method for solving partial differential equations

#### Competences

• Must be able toengage in adialogue regarding theoptimal choiceof analytical and numericalsolutionmethods forpartial differential equations, andresults frommathematicalmodelingin general
• Must be able to disseminatesetupandresultsofsolvingcertainpartial differential equationsto others, includingcolleagues, government agencies and others.

### Type of instruction

• Lectures supplemented with project

150 hours

## Exam

### Exams

 Name of exam Mathematical Modeling and Numerical Methods Type of exam Written 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