310-3040/02 – Mathematical modeling of engineering problems (MMIU)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | Mgr. Ivona Tomečková, Ph.D. | Subject version guarantor | Mgr. Ivona Tomečková, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FMT | Intended for study types | Master, Follow-up Master |
Subject aims expressed by acquired skills and competences
Students will learn a structural approach to the mathematical formulation of engineering practice problems.
The acquired knowledge will then be used to analyse of specific tasks via
- mathematical formulation through a system of differential equations,
- recognizing the appropriate calculation method,
- the correct calculation of the mathematical issue and
- a final meaningful interpretation of the results.
Teaching methods
Lectures
Individual consultations
Tutorials
Project work
Summary
The course offers a unified view of mathematical modeling of physical states and processes with a focus on tasks described by differential equations. Applications are devoted to the solving real problems of engineering practice with regard to the prevailing professional focus of students. Students' knowledge of some mathematical software is assumed, for example MatLab, to get the result or its visualization.
Compulsory literature:
William E.: Partial Differential Equation Analysis in Biomedical Engineering - Case Studies with MATLAB, 2013
Kulakowski, Bohdan T.; Gardner, John F.; Shearer, J. Lowen: Dynamic Modeling and Control of Engineering Systems, 3rd Edition, 2007
Mathematical Modelling: Classroom Notes in Applied Mathematics (Ed. M.S. Klamkin). SIAM Philadelphia, 3rd printing, 1995.
Recommended literature:
Friedman A., Littman W.: Industrial Mathematics. SIAM, 1994.
Lawson D., Marion G.: An Introduction to Mathematical Modelling,
a course text: https://people.maths.bris.ac.uk/~madjl/course_text.pdf
Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013
Additional study materials
Way of continuous check of knowledge in the course of semester
Course-credit:
-participation on tutorials is obligatory, 20% of absence can be apologized,
-pass one credit test (maximum 30 points, required at least 10 points).
Exam
Semestral thesis classified by 25 – 50 points.
An oral theoretical part of the exam is classified by 0 - 20 points.
E-learning
Other requirements
Elaboration of a semestral project
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Principles of mathematical modeling. Model quantities.
Basic relations, local and global balance.
One-dimensional stationary states.
Classification of boundary problems. Corectness of mathematical model.
Non-stationary processes - one-dimensional case. Initial problems.
First order PDE. Method of characteristics.
Application - free and thermal convection.
PDE of second order: classification, Fourier method.
Fourier method for parabolic and hyperbolic PDE.
Multi-dimensional stationary states.
Fourier method for elliptic PDE. Boundary problems for multivariate problems.
Numerical methods - a brief introduction (optional)
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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