M6868 Diffrential Equations and Their Applications

Faculty of Science
Spring 2010
Extent and Intensity
2/2. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M6868/01: Tue 10:00–11:50 M3,01023, 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 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
Final written test - solution of a not very difficult 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 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (Spring 2010, recent)
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