(Created 2009-08-11.)
 MATHEMATICAL MODELLING FMA045

Higher education credits: 4,5. Grading scale: UG. Level: G1 (First level). Language of instruction: The course will be given in Swedish. Compulsory for: Pi1. Course coordinator: Studierektor, Lars-Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Recommended prerequisits: Linear algebra. The first part of the calculus course. Assessment: Written and oral report of project work, individually and group-wise. Compulsory attendance at the project reports. Take home exam on Matlab. Parts: 2. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The aim of the course is to arouse awareness of the problems of mathematical modelling, i.e., what it means to create quantitative models which can give understanding of phenomena in reality. A further aim is that the student should learn to master some general tools and structures which can be used in modelling, and learn engineering ways of thinking. The course should also provide acquaintance with Matlab and its use for simulation and computation. Furthermore, the course should develop the student's abilities in oral and written presentation.

Knowledge and understanding
For a passing grade the student must

be able to clearly explain and use the basic concepts of mathematical modelling, in particular be able to explain what a mathematical model is.

be able to describe and informally explain the process of mathematical modelling, including identification of the problem, formulation, analysis, computation, simulation and feed-back.

be able to use basic concepts in Matlab programming, such as numbers, vectors, matrices, iteration, scripts, functions, and with confidence be able to carry out simple computations on a computer.

Skills and abilities
For a passing grade the student must

independently or group-wise be able to apply the mathematical modelling process on simple and realistic, but vaguely formulated problems, of which some is connected to environment. More specifically, the student should show good ability to:

• identify and judge how different factors affect a system,

• formulate a problem in mathematical terms, equations and constraints,

• judge the validity and limitations of a model, and how it can be refined,

• analyse and carry out simple simulations on a model,

• consider and interpret the solution model in relation to the original problem, and judge the validity and limitations of the solution.

independently, using appropriate documentation, be able to write Matlab programs to solve mathematical problems in the framework of the course.

in writing as well as orally, with proper terminology, in a well structured way and with clear logic be able to explain the solution to a modelling problem.

Judgement and approach
For a passing grade the student must

develop an attitude to the world around us and mathematics, where the usefulness of mathematics in quantitative descriptions of reality seems natural and possible.

be able to tolerate redundance in or missing data, and in such cases to have an engineering attitude in making considerations.

Contents
Modelling: The couplings between model and reality. Validation of a model. Some modelling tools.

Basic Matlab programming: Numbers, vectors, matrices, iteration, the work area, scipts, functions. Visualisation.

Literature
Åström & Sparr: Matematisk modellering. Matematikcentrum 2005.
Pärt-Enander & Sjöberg: Användarhandledning för MATLAB 6.5. Uppsala universitet, avd för TDB. ISBN 91-506-1690-0.

Parts

Code: 0107. Name: Mathematical Modelling.
Higher education credits: 3,5. Grading scale: UG. Assessment: Written and oral reports on project work, individually and groupwise. Compulsory attendance at the presentations of project reports. Contents: The couplings between model and reality. Validation of a model. Some modelling tools.

Code: 0207. Name: Basic Matlab Programming.
Higher education credits: 1. Grading scale: UG. Assessment: Home exam on a computer. Contents: Numbers, vectors, matrices, iteration, the work area, scipts, functions. Visualisation.