Mathematical Modeling and Numerical Methods

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

Extent and expected workload

150 hours

Exam

Exams

Name of examMathematical Modeling and Numerical Methods
Type of exam
Written or oral 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-B5-6
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