Mathematical modelling (2024)

Course manager

Kresten Troelstrup Meisler

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, enzyme technology 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. Mathematical modelling 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
• Transfer functions
• Modelling and simulation of chemical, mechanical, and biological 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 and transfer functions

Skills

• Convert physical conditions into a mathematical model by way of an equation and/or a system of  equations
• Apply Laplace transformations in the solution of differential equations
• Set up and solve n^th order differential equations
• Investigate relations in data through statistical methods
• 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 

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. 

Google Colab and Google Drive are permitted. No other internet access is allowed.

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

Marking 

External

Grading

7-point grading scale