Bi3101 Mathematical modelling - introduction

Faculty of Science
Autumn 2020
Extent and Intensity
2/0/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. et Mgr. Jiří Kalina, Ph.D. (lecturer)
Guaranteed by
Mgr. et Mgr. Jiří Kalina, Ph.D.
RECETOX – Faculty of Science
Contact Person: Mgr. et Mgr. Jiří Kalina, Ph.D.
Supplier department: RECETOX – Faculty of Science
Timetable
Mon 8:00–9:50 D29/347-RCX2
Prerequisites
Basic knowledge of mathematical analysis and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is for students to adopt methods of building and solving simple mathematical models, including an interpretation of obtained results and estimation of their possible errors. An overview of available software tools, their advantages and disadvantages is provided to the students as well as possibilities of execute computationally demanding models on a grid infrastructure.
Learning outcomes
At the end of the course, students are able to: - to build simple mathematical models, - to solve mathematical models using appropriate software, - to analyze obtained results and their errors and to interpret them, - to execute complex calculations in MetaCentrum Distributed Computing Infrastructure (NGI).
Syllabus
  • The mathematical model definition, process of modelling and simulation, phases of mathematical model building.
  • Input data of the model, simplifying assumptions, problem definition, initial and edge conditions.
  • Software for mathematical modelling, introduction of tools for building and solving models (Matlab, Maple, R etc.), their advantages and disadvantages.
  • Mathematical model proposal, correctness analysis and solving method proposal. Analytical and approximate solutions.
  • Model implementation using the software tools and its solution using a computer. Testing of the models.
  • Sensitivity and uncertainty analysis of the models. Visualization of obtained results, evaluation of solutions and their errors.
  • Selected examples of biological problems and methodology of their solving.
  • Solving computationally demanding models using the national grid infrastructure MetaCentrum.
Literature
    required literature
  • HŘEBÍČEK, Jiří, Zdeněk POSPÍŠIL and Jaroslav URBÁNEK. Úvod do matematického modelování s využitím Maple (Introduction to Mathematical Modelling Using Maple). první. Brno: Akademické nakladatelství CERM, 2010, 120 pp. ISBN 978-80-7204-691-1. info
    recommended literature
  • GANDER, Walter and Jiří HŘEBÍČEK. Solving Problems in Scientific Computing Using Maple and MATLAB. čtvrté. Heidelberg: Springer, 2004, 476 pp. Mathematics. ISBN 3-540-21127-6. URL info
Teaching methods
Interactive lectures with a work on computers, 4 homeworks during the semester.
Assessment methods
Lectures are presented weekly in semester. During the semester, 4 homeworks are assigned. Processing of the homeworks is a necessary condition of passing an examination on a computer.
Language of instruction
Czech
Follow-Up Courses
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 2018, Autumn 2019, autumn 2021.
  • Enrolment Statistics (Autumn 2020, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2020/Bi3101