E3101 Mathematical modelling - introduction

Faculty of Science
Autumn 2023
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
Thu 13:00–14:50 F01B1/709
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 software R + Rstudio, - 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, 5 homeworks during the semester and 6th homework over Christmas.
Assessment methods
Lectures are presented weekly in semester. During the semester, 6 homeworks are assigned. Evaluation of the homeworks is part of the overall evaluation of the course. The course is finished by an exam written on computers.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The course starts by its first lecture on 25th September 2023. The course takes place in a computer lecture room but it is possible to work also on your own computer.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/E3101