M7111 Topics on mathematical modelling

Faculty of Science
Autumn 2018
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: k (colloquium).
Teacher(s)
doc. RNDr. Petr Lánský, DrSc. (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 17. 9. to Fri 14. 12. Thu 12:00–13:50 M6,01011
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Selected methods of mathematical modeling are presented and developed. A comparison between deterministic and stochastic approaches is followed in detail. New trends in mathematical modeling are introduced and reviewed. Each chapter is supplemented by a summary of applied mathematical procedures.
After passing the course, the student will be able:
to define and interpret the basic notions used in the basic parts of mathematical modeling and to explain their mutual context;
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques utilized in basic fields of mathematical modeling;
to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • Program is modified with respect to models under consideration 1) Hypergeometric probability distribution 2) Poisson probability distribution 3) Random variable simulation 4) Poisson process, in time and space 5) Sequences of random variables 5) Information coding 6) Birth-and-death processes 7) Deterministic population models 8) Diffusion processes 9) Stochastic differential equations
Literature
  • TUCKWELL, Henry C. Elementary applications of probability theory : with an introduction to stochastic differential equations. 2nd ed. London: Chapman and Hall, 1995, xv, 292. ISBN 0412576201. info
Teaching methods
Lectures and discussion
Assessment methods
Active discussion during lectures, cooperation during classes. To conclude the term, one has to prove understanding the topics, to be able to create new concepts and this has to be shown in the homeworks.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2018, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2018/M7111