Mathematics in the Life Sciences
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WBLS16000 
Vaknaam  Mathematics in the Life Sciences 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Mathematics in the Life Sciences  
Leerdoelen  The student is able to: (1} apply basic mathematical techniques (including differentiation, integration, multivariate analysis, qualitative analysis of dynamical systems, and bifurcation analysis) to dynamical and optimality models in the life sciences; (2} solve mathematical problems in the life sciences with the help of technical computing software (Mathematica). 

Omschrijving  The course will:  train basic mathematical skills, such as differentiation and integration;  introduce students to important mathematical concepts and methods, such as complex numbers, linear algebra, multivariate analysis, and linearization techniques;  provide insight into the use and interpretation of dynamical models in the life sciences;  expose students to important classes of example models in the life sciences;  teach students how to investigate dynamical models with analytical and numerical methods;  expose students to more advanced concepts and methods, such as chaotic attractors and bifurcation analysis;  teach students how to solve mathematical problems with the help of technical computing software ( M athematica). The first week of the course will focus on mathematical key concepts (like differentiation, integration, Taylor expansion) and on the analysis of onedimensional dynamical systems (single ordinary differential equations (ODEs) and single recurrence equations). Student will learn how to solve these systems either analytically or numerically, both with pencil and paper and with a programme like M athematica, and to perform an equilibrium and stability analysis. Students will also be exposed to bifurcation analysis, catastrophes, and chaotic attractors. In the second week, complex numbers and concepts of linear algebra (eigenvalues and eigenvectors) will be introduced. Students will learn the basics of multivariate analysis, including multivariate optimization (Hessian). These techniques will allow them to analyse simple stochastic systems, like Markov processes. Students also learn how to analyse 2nd_ order ODEs and recurrence equations. The third week is devoted to systems of ODEs and recurrence equations. Students learn how to solve linear systems analytically, how to solve nonlinear systems numerically, and how to conduct a qualitative analysis of a multidimensional dynamical system (equilibrium and stability analysis). 

Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Practisch werk (PRC)
(Lectures (70 h), computer practicals (70 h)) 

Toetsvorm 
Practisch werk (PR)
(Weekly assignments and exercises. The first two assignments have a weight of 25% each while the third (overarching) assignment has a weight of 50%. To pass the course, the final grade for course needs to be a 6.0 or higher.) 

Vaksoort  bachelor  
Coördinator  prof. dr. R.S. Etienne  
Docent(en)  prof. dr. R.S. Etienne ,prof. dr. F.J. Weissing  
Verplichte literatuur 


Entreevoorwaarden  
Opmerkingen  Maximum capacity: 24 students. This course is also open to students outside the minor programme. Students who have completed this course will be considered to fulfil the entry requirements for Biological Modelling and Model Analysis (WBLS16001). 

Opgenomen in 
