M6868 Continuous deterministic models II

Faculty of Science
Spring 2014
Extent and Intensity
2/2. 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)
Mgr. Veronika Bernhauerová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 12:00–13:50 M2,01021
  • Timetable of Seminar Groups:
M6868/01: Tue 18:00–19:50 M5,01013, V. Bernhauerová
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 ODE theory;
to apply the results to selected applications in life sciences.
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
  • BRITTON, Nicholas F. Essential mathematical biology. London: Springer, 2003, xv, 335 s. ISBN 1-85233-536-X. info
  • FRANCŮ, Jan. Parciální diferenciální rovnice [Franců, 2003]. 3. vyd. Brno: CERM, 2003, 155 s. ISBN 80-214-2334-X. info
  • MURRAY, J. D. Mathematical biology. 1st ed. New York: Springer-Verlag, 1989, xiv, 767. ISBN 0387194606. info
  • M.Kot, Elements of Mathematical Ecology, Cambridge, 2001
  • Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics.Dordrecht-Boston-London: Kluwer, 1992.501 s. Mathematics and Its Applications; vol. 74. ISBN 0-7923-1594-4.
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
Study Materials
The course is taught once in two years.
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 2016, spring 2018, Spring 2020, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (Spring 2014, recent)
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