310-4002/02 – Mathematical modeling of engineering problems (MMIU)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFS, FMTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 20+0
Part-time Examination 20+0

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
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 and its toolboxes.

Compulsory literature:

Vlček, J.: Mathematical modeling, http://homen.vsb.cz/~vlc20/ Mathematical Modelling (Ed. M.S. Klamkin). SIAM, 1989. Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013

Recommended literature:

Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994. Keener, J. P.: Principles of Applied Mathematics. Adison-Wesley Publ. Comp. 1994

Way of continuous check of knowledge in the course of semester

Oral examination.

E-learning

http://mdg.vsb.cz/portal

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. Model quantities. 2. Basic relations, local and global balance. 3. One-dimensional stationary states. 4. 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. Facultative themes.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)		Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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