310-3340/02 – Mathematical Modelling (MM)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | Mgr. Ivona Tomečková, Ph.D. | Subject version guarantor | Mgr. Ivona Tomečková, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Master, Follow-up Master |
Subject aims expressed by acquired skills and competences
Students will learn a structural approach to move from meaningful physical assumptions and observed conclusions to mathematical problems known from previous studies and engineering practice.
The acquired knowledge will then be used to analyse of specific tasks via
- a suitable mathematical formulation through differential equations,
- recognizing the appropriate calculation method and the correct calculation of the mathematical issue and
- a final meaningful physical 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:
[1]
William E.: Partial Differential Equation Analysis in Biomedical Engineering - Case Studies with MATLAB, 2013
[2]
Kulakowski, Bohdan T.; Gardner, John F.; Shearer, J. Lowen: Dynamic Modeling and Control of Engineering Systems, 3rd Edition, 2007
[3]
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
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 the credit test (maximum 30 points, required at least 10 points),
Point classification: 0-30 points.
Exam
Semestral thesis classified up to 50 points.
Theoretical up to 20 points.
E-learning
Other requirements
For additional requirements see www.mdg.vsb.cz
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.
Method of characteristics for the PDEs of the first order.
Application - free thermal convection.
PDEs of the second order: classification, Fourier method.
Fourier method for parabolic and hyperbolic PDEs.
Multi-dimensional stationary states.
Fourier method for elliptic PDEs. Boundary problems for multivariate problems.
Facultative themes.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.