M6868 Continuous deterministic models II

Faculty of Science
spring 2018
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)
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
Mon 16:00–17:50 M6,01011
  • Timetable of Seminar Groups:
M6868/01: Mon 18:00–19:50 M6,01011, 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
  • FRANCŮ, Jan. Parciální diferenciální rovnice [Franců, 2003]. 3. vyd. Brno: CERM. 155 s. ISBN 80-214-2334-X. 2003. info
  • SMITH, Hal L. An introduction to delay differential equations with applications to the life sciences. Dordrecht: Springer. xi, 172. ISBN 9781441976451. 2011. info
  • BRITTON, Nicholas F. Essential mathematical biology. London: Springer. xv, 335 s. ISBN 1-85233-536-X. 2003. info
  • KOT, Mark. Elements of mathematical ecology. Cambridge: Cambridge University Press. ix, 453. ISBN 9780521001502. 2001. info
  • MURRAY, J. D. Mathematical biology. 1st ed. New York: Springer-Verlag. xiv, 767. ISBN 0387194606. 1989. 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
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 2014, Spring 2016, Spring 2020, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (spring 2018, recent)
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