714-0766/02 – Mathematical modeling of engineering problems (MMIU)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 3 |
| Subject guarantor | doc. RNDr. Jaroslav Vlček, CSc. | Subject version guarantor | doc. RNDr. Jaroslav Vlček, CSc. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2013/2014 | Year of cancellation | 2019/2020 |
| Intended for the faculties | HGF, FMT, USP | Intended for study types | Follow-up Master, Master |
Subject aims expressed by acquired skills and competences
Students learn structural approach to mathematical formulation of engineering problems.
They shlould know how
to analyze given problem,
to formulate mathematical task,
to choose and correctly use appropriate mathematical method.
Teaching methods
Lectures
Individual consultations
Tutorials
Project work
Summary
The topic offers a complex view on mathematical modeling of physical states and
processes with emphasized orientation to the problems described by differential
equations. Applications are devoted to the solving of real problems comming out
from engineering praxis in regard to prevailing student specialization. The use of mathematical software is assumed,e.g. MATLAB.
Compulsory literature:
Vlček, J.: Mathematical modeling, http://homen.vsb.cz/~vlc20/
Mathematical Modelling (Ed. M.S. Klamkin). SIAM, 1989.
Recommended literature:
Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994.
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 the written test (30 points),
Point classification: 0-30 points.
Exam
Semestral thesis classified by 25 – 50 points.
Theoretical part of the exam is classified by 0 - 20 points.
E-learning
www.mdg.vsb.cz
Other requirements
Elaboration of semestral project
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Principles of mathematical modeling.
2. State, flow, material and source quantities.
3. Basic relations: balance and constitutive.
4. Local and global balance.
5. Classification of boundary problems. Corectness of mathematical model.
6. One-dimensional stationary states.
7. Multi-dimensional stationary states.
8. PDE of second order: classification, Fourier method.
9. Non-stationary processes - one-dimensional case.
10. First order PDE. Method of characteristics.
11. Initial problems for multivariate problems.
12. Facultative themes
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction