Mathematical modelling (2021)
Christian Møller Pedersen
Spring (13-week period)
Language of instruction
Competences corresponding to participation in the courses – Mathematics 1 and Statistics, Physical chemistry and Chemical engineering – are recommended.
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.
- 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.
On completion of the course, the student is expected to be able to:
- Understand and explain the principles of the set-up and solution of differential equations and systems thereof
- Understand and explain Laplace transformations
- 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.
- 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
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.
7-point grading scale