M6868 Continuous deterministic models II

Faculty of Science
Spring 2024
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: k (colloquium). Other types of completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Guaranteed by
prof. RNDr. Zdeněk Pospíšil, Dr.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Tue 16:00–17:50 M4,01024
  • Timetable of Seminar Groups:
M6868/01: Mon 19. 2. to Sun 26. 5. Tue 18:00–19:50 M4,01024, Z. Pospíšil
Prerequisites
Any course of calculus and linear algebra, a basic course of ordinary differential equations
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Main objectives of this course are:
to understand the fundamentals of PDE theory;
to introduce some advanced topics in delay ODE theory;
to apply the results to selected applications in life sciences.
Learning outcomes
Successful getting through the course allows a student:
- to express a structured real-world process going on a continuous time by means of partial differential equation;
- to model a real-world process with a memory by means of delay differential equations;
- to analyze these model in a qualitative way;
- to interpret obtained results.
Syllabus
  • 1. First order linear partial differential equations; population model with age distribution. 2. Second order partial differential equations, parabolic equation, separation of variables; spatially structured population models. 3. Reaction-diffusion; models of morphogenesis. 4. Delay ordinary differential equations; delay population models, delay models in physiology.
Literature
  • FRANCŮ, Jan. Parciální diferenciální rovnice [Franců, 2003]. 3. vyd. Brno: CERM, 2003, 155 s. ISBN 80-214-2334-X. info
  • SMITH, Hal L. An introduction to delay differential equations with applications to the life sciences. Dordrecht: Springer, 2011, xi, 172. ISBN 9781441976451. info
  • BRITTON, Nicholas F. Essential mathematical biology. London: Springer, 2003, xv, 335 s. ISBN 1-85233-536-X. info
  • KOT, Mark. Elements of mathematical ecology. Cambridge: Cambridge University Press, 2001, ix, 453. ISBN 9780521001502. info
  • MURRAY, J. D. Mathematical biology. 1st ed. New York: Springer-Verlag, 1989, xiv, 767. ISBN 0387194606. info
Teaching methods
Lectures; class exercises consisting in solution of selected problems.
Assessment methods
Colloquium consists in solution of a selected problem.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2004, Spring 2006, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2023.
  • Enrolment Statistics (recent)
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