1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Introduction to Mathematical Modelling

Wygeneruj PDF dla tej strony

Introduction to Mathematical Modelling - opis przedmiotu

Cel przedmiotu

The purpose of the course is to familiarize students with the nature, scope and stages of mathematical modeling. The lecture will present a broad overview of mathematical models and methods used in technical, economic, biological or social problems. The goal of the project class is to simulate the presented models using a selected programming language (e.g. Python). After completing this course, the student should be prepared to create simple mathematical models using computers and their mathematical knowledge.

Wymagania wstępne

Zapisz zmiany

Mathematical analysis

Zakres tematyczny

Lecture/project:

1. The aim, scope and stages of mathematical modeling of engineering problems. The role of numerical methods.
2. Discrete and continuous mathematical models - construction, solution, analysis and validation.
3. Review of mathematical models and methods used to solve selected technical, economic, biological or social problems.
4. Application of a selected mathematical package in the simulation process of solutions to the given engineering problems.

Metody kształcenia

Lecture: traditional and problem-based, available in electronic form.
Project: solving computational tasks using a selected programming language (e.g., Python); discussion of the selecting problem of numerical method appropriate to the problem under consideration and the complexity of the computational error.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The basic form of passing the lecture in this course is a colloquium, which includes mathematical modeling of the problems presented in the lecture, analysis of the obtained solutions and highlighting the mathematical methods used in the modeling process. The grade for the project will be determined by the total number of points obtained from all the mini-projects that the student will have to prepare independently. The grade for the course consists of the grade from the project (40%) and the grade from the colloquium (60%). The condition for passing the course is a positive grade from both the project and the lecture.

Literatura podstawowa

1. B. Burnes, G. R. Fulford, Mathematical modeling with case studies, Taylor and Francis, 2002.
2. J. D. Murray, Mathematical Biology.  An Introduction, Springer, 2002.
3. G. R. Fulford, P. Broadbridge, Industrial Mathematics, Cambridge University Press, 2002.
4. G. R. Fulford, P. Forrester, A. Jones, Modelling with Differential and Difference Equations, Cambridge University Press, 1997.
5. D. Kincaid, W. Cheney, Numerical Analysis. Mathematics of Scientific Computing, The University of Texas at Austin, 2002.

Literatura uzupełniająca

1. A. Quarteroni, F.Saleri, Scientific Computing with Matlab and Octave, Springer, 2006;
2. J. D. Logan,  Applied mathematics, a contemporary approach, John Wiley and Sons, New York, 2001.
3. A. Björck, G. Dahlquist, Numerical Methods in Scientific Computing, SIAM, 2008.
4. G. R. Fulford, P. Broadbridge, Industrial Mathematics, Cambridge University Press, 2002.

Uwagi

Subject also offered in semester VI.

Zmodyfikowane przez dr Maciej Niedziela (ostatnia modyfikacja: 07-02-2024 22:09)