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Syllabus for

Academic year
DAT025 - Mathematical modelling
 
Owner: TITEA
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: A
Department: 37 - COMPUTER SCIENCE AND ENGINEERING


Teaching language: Swedish

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0105 Laboratory 0,0 c Grading: UG   0,0 c    
0205 Written and oral assignments 5,0 c Grading: TH   5,0 c    

In programs

TM Teknisk matematik, Year 2 (elective)
TITEA SOFTWARE ENGINEERING, Year 2 (compulsory)
TDATA COMPUTER SCIENCE AND ENGINEERING - Other elective courses, Year 4 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)

Examiner:

Docent  Dag Wedelin



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

The compulsory courses in mathematics on the IT-program or their equivalent (i.e. discrete mathematics, linear algebra, analysis and mathematical statistics). Algorithms is a course that complements this course in a nice way, but is not a requirement.

Aim

Modelling, i.e. to create an abstract model - or description - of a physical or logical reality, is a basic tool in science and engineering. A model makes it possible to represent, understand, simulate and optimize the structure, appearance or behavior of a real system.

The ability to apply IT in different areas is essential for an engineer in the information systems area. This can be in traditional engineering disciplines as well as in other areas, such as economy, medicine and games, where the variation in the problems and appropriate ways of approaching them is considerable.

Goal

The goal of the course is therefore to show how mathematics can be used in this context, and to give an ability to understand and select appropriate models for different real systems and structures. It thus connects what you learn in theoretical courses in mathematics, with different applications.

Content

The core of the course is a number of carefully selected exercises, to develop the skill of using mathematics to solve real problems. These are grouped after the main model types:

* Functions and equations. The significance of different kinds of mathematical expressions and how they can be motivated. How to find and fit functions to empirical data. Curves in computer graphics.
* Optimization models. Mathematical programming in economics and decision support.
* Dynamic models. Simulation in biology, physics and engineering.
* Probability models. Stochastic simulation. Markovmodels for texts, language and expert systems.
* Discrete models. Graphs and networks for modelling projects and activities, modelling with discrete standard problems and boolean logic, planning.
* Modelling languages. For optimization and rule based expert systems.

The exercises consider realistc examples and are chosen to devlop the skill of modelling, and at the same time learn the most important properties and limitations of the different model types. When possible, different ways to model the same problem are compared. The course also explains the potential and usefulness of building computer models for different kinds of applications.

Organisation

The course is organized in weekly modules, one for every model type. This consists of an introductury lecture, exercises for the week, and a follow-up exercise giving feedback to the solved exrecises. The exercises are done in groups of two persons. The course also contains introductory and final lectures, and a guest lecture.

Literature

Since the exercises are the core of the course we have not selected any compulsory course literature. For anyone who still wishes a couse book, we can recommend Giordano et.al. : A first course in mathematical modeling (3rd ed).

Examination

The course ends with an individual summarizing report. Passed exercise assignments.


Page manager Published: Mon 28 Nov 2016.