Syllabus academic year 2011/2012
(Created 2011-09-01.)
BIOMATHEMATICSFMAN01
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course might be given in English. Optional for: E4, E4mt, F4, F4bm, Pi4, Pi4bm, W4ms. Course coordinator: Director of Studies, Anders Holst, ah@maths.lth.se and Anders Heyden, heyden@maths.lth.se, Mathematics. Recommended prerequisits: Courses in applied mathematics, e.g. FMAF10 and FMAF15. The course might be cancelled if the number of applicants is less than 10. Assessment: Compulsory assignments. Approved results on these are enough to pass the course. To get a higher grade it is required to pass a written and an oral examination.

Aim
The main aim of the course is to give a basic introduction to mathematical theory and methods in biology, with enough scope to enable the student to handle biologically phrased problems. An additional aim is to help the student develop his or her ability in problem solving, with or without a computer. A further aim is to prepare the student for further studies in e.g. biological systems or evolution biology.

Knowledge and understanding
For a passing grade the student must

be able to present clearly and independently use basic mathematical concepts in biology, in particular regarding cell modelling, evolution dynamics and diffusion phenomena.

be able to present and give an informal explanation of the mathematical theory behind some central biological models, such as non-linear difference equations, non-linear differential equations and reaction-diffusion equations.

Skills and abilities
For a passing grade the student must

be able to use computer packages to simulate solutions to biological problems.

be able to show good capability to independently identify biological problems which can be solved with mathematical modelling, and be able to choose an appropriate method.

be able to independently apply basic modelling to biological problems which are relevant in industrial applications and research.

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

Contents
Population growth. Non-linear difference equations. Evolution dynamics. Continuous models. Phase plane methods. Molecule dynamics. The cell cycle. Limit cycles, oscillations and excitable systems. Modelling of diffusion. PDE-models. Pattern formation.

Literature
Edelstein-Keshet, L: Mathematical Models in Biology, SIAM 2004 ISBN 0-07-554950-6.