Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-84-11-M-7

Biomathematics (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-84-11-M-7 Biomathematics 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-84-11-K-7
Biomathematics
P 84 h 186 h - - PL1 9.0 irreg.
  • About [MAT-84-11-K-7]: Title: "Biomathematics"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86152 ("Biomathematics")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • qualitative analysis of ordinary differential equations, nondimensionalization, stability and bifurcation.Applications: enzyme kinetics due to the Law of mass action, population interaction models (e.g.predator-prey model, cooperation/symbiosis, concurrence),
  • diffusion and transport processes, random walks and partial differential equations;· traveling waves, perturbation solutions, similarity solutions, asymptotic methods,
  • reaction-diffusion (transport) equations, chemo- and haptotaxis as cell migrations,
  • comparison principles, invariant sets and global solvability,
  • structured population models,
  • kinetic transport equations for cell migration problems, macroscopic scaling. Applications: Pattern formation in animals, cancer cell invasion and migration of tumor cells throughtissue networks, epidermal wound healing.

Competencies / intended learning achievements

Based on problems from the field of Biology and Medicine, students have learnt how to set up mathematical models in which they focus on essential aspects of such problems. They have learnt how to apply advanced tools from ordinary and partial differential equations to the derived problems to be able to make predictions about concrete biological phenomena and to interpret the results. They are able to name the essential statements of the lecture as well as to classify and to explain the connections.

By completing the given exercises, the students have gained experience in dealing with the introduced mathematical objects and methods and insights into interdisciplinary problems.

Literature

  • J.D. Murray: Mathematical Biology I, II,
  • S.H. Strogatz: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering,
  • J. Smoller: Shock Waves and Reaction-Diffusion Equations.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Additional knowledge from the module [MAT-80-11B-M-4] is useful but not necessarily required.

Modules:

Courses

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-84-11-M-7]

Module-Pool Name
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)