Mathematical models in natural sciences 1000-716MNP
Course content:
Presentation of the basic methods of analysis of dynamical systems with continuous time (differential equations) and with discrete time (differential equations): solving systems of linear equations, methods of analysing nonlinear systems.
Discrete dynamical systems: an overview of the possible types of trajectory behaviour.
Ordinary differential equations: the simplest methods of integration, integral and phase curves, stability, phase portraits.
Applications of dynamical systems to describe various phenomena – presentation and analysis of selected mathematical models: dynamics of a single population, interactions between populations, protein production, epidemic course.
Indication of similarities and differences between continuous and discrete description on the example of selected models.
Learn about the most important linear partial differential equations of two variables. Reaction-diffusion equations.
As part of the laboratory: getting to know Matlab and Mathematica packages for numerical solving and graphical presentation of solutions to difference and differential equations.
Type of course
Course coordinators
Learning outcomes
Student finishing the course:
1) has knowledge of the basic methods of analysis od dynamical systems with continuous and discrete time,
2) knows selected mathematical models describing various natural phenomena,
3) is able to use selected mathematical packages (Maple, Matlab) to numerically solve differential equations and graphical representation of their solutions.
4) is able to apply mathematical methods to describe natural phenomena, is able to draw conclusions from specific models and is aware of the limitations of the methods used.
Assessment criteria
FINAL SCORE WILL BE GIVEN ON THE BASIS OF:
- points from classes – 70 points: short tests 40 points, activity during classes 30 points,
- points from labs (short problems to solve) – 30 points,
- written exam on difference and ordinanry differential equations (solving linear equations, solving differential equations of selected types, analysis of difference and differential equations) – 100 points.
For a positive grade, it is necessary to obtain more than 50% of the points.
Zero exam will be available to students who obtain a minimum of 80 points for classes (exercises + laboratory).
Re-take exam: the grade will be given only on the basis of the exam.
Bibliography
J.D. Murray: Mathematical biology I: An introduction
J.D. Murray: Mathematical biology II: Spatial models and biomedical applications
Notes
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Term 2023Z:
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Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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