Mathematical modelling (2021)

Course manager

Christian Møller Pedersen

Semester schedule

Spring (13-week period)

ECTS

5

Language of instruction

English

Course type

Compulsory

Qualifications

Competences corresponding to participation in the courses – Mathematics 1 and Statistics, Physical chemistry and Chemical engineering – are recommended.

Objectives

Computer-based calculation methods are – to a great extent – applied for the purposes of performing engineering modelling and analysis of complex physical, chemical, biotechnological and process-technological interrelations. For the purpose of obtaining the maximum benefit from such calculation methods, it is important to possess detailed knowledge about the theoretical background. Applied mathematics 1 is targeted at familiarising the students with the part of mathematics that constitutes the foundation for these advanced computer-based calculation methods.

Content

  • Ordinary differential equations
  • Systems of ordinary differential equations
  • Laplace transformations
  • Phase plane analysis
  • Simple modelling and simulation of chemical, biological, thermal or mechanical systems by use of Python.

Learning targets

On completion of the course, the student is expected to be able to:

Knowledge

  • Understand and explain the principles of the set-up and solution of differential equations and systems thereof
  • Understand and explain Laplace transformations

Skills

  • Convert physical conditions into a mathematical model by way of a dimensionsless differential equation and/or a system of differential equations
  • Apply Laplace- or Fourier transformations in the solution of differential equations
  • Set up systems of differential equations in matrix form
  • Set up and solve nth order differential equations
  • Predict the result of e.g. a given fermentation system by simple modelling and simulation of the processes
  • Set up and apply mathematical models for calculation and simulation of relevant parameteres for chemical, biological, thermal or mechanical systems. 

Competences

  • Master different solution techniques for various types of differential equations/systems of differential equations, be they analytical or numeric
  • Master software that can be applied for numerical solution of ordinary differential equations 

Teaching method

Seminars and problem solution.

Qualifications for examination participation

  •  Approval of all written assignments

All shall be executed and submitted pursuant to guidelines set out by the course manager.

Examination and aids

Written examination. Duration of examination: 4 hours.

Permitted aids: Text book, notes and mathematical program/spreadsheet. No access to the internet. 

The form of examination at a 3rd attempt may vary from the above.

Marking 

External

Grading

7-point grading scale