Mathematical Modeling and Numerical Methods

2018/2019

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

Extent and expected workload

150 hours

Exam

Exams

Name of examMathematical Modeling and Numerical Methods
Type of exam
Written exam
ECTS5
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentAs stated in the Joint Programme Regulations

Facts about the module

Danish titleMatematisk modellering og numeriske metoder
Module codeK-KT-B5-31
Module typeCourse
Duration1 semester
SemesterAutumn
ECTS5
Language of instructionEnglish
Empty-place SchemeYes
Location of the lectureCampus Esbjerg
Responsible for the module

Organisation

Study BoardStudy Board of Biotechnology, Chemistry and Environmental Engineering
FacultyFaculty of Engineering and Science