470-8341/01 – Selected Chapters from Mathematics (VKM)

Gurantor departmentDepartment of Applied MathematicsCredits5
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFSIntended for study typesMaster, Follow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
FOL0037 Ing. Ladislav Foltyn
HOR33 doc. Ing. David Horák, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
MAR440 Ing. Alexandros Markopoulos, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Combined Credit and Examination 10+0

Subject aims expressed by acquired skills and competences

Student will understand model partial differential equations, basic methods of approximation of the solution of the boundary value problems, variational equalities and inequalities, their abstract structure and methods of solution. He/she will understand the role of these conceps in applications.

Teaching methods

Lectures
Tutorials

Summary

Successful solution of the problems arising in engineering requires anunderstanding of relevant mathematics. The students will learn about basic tools and their applications for the solution of such problems.

Compulsory literature:

K. Rektorys, Variational Methods in Mathematics, Science and Engineering. Reidel, Dordrecht, 1980

Recommended literature:

G. Strang, Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986. ISBN-13: 9780961408800

Way of continuous check of knowledge in the course of semester

Test Written and oral exam

E-learning

Další požadavky na studenta

Additional requirements for students are not.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Boundary value problems for ordinary differential equations of the 2nd order. Finite difference discretization and boundary conditions. Problems with non-smooth soefficients and/or right hand side. Variational formulation of the boundary value problems. Discretization based on variational formulation. Collocation, Ritz method, Galerkin method, finite element method. Propertis and direct methods of solution of the discretized systems. Conjugate gradient method with preconditioning. Domain decomposition and multilevel methods. Variational inequalities and their discretization. Numerical solution of variational inequalities. Boundary integral equations. Bouhary element method for a model problem. Software.

Conditions for subject completion

Full-time form (validity from: 2012/2013 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30  15
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
2018/2019 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2018/2019 (N2301) Mechanical Engineering (3901T003) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
2017/2018 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2017/2018 (N2301) Mechanical Engineering (3901T003) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
2016/2017 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2015/2016 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2014/2015 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2013/2014 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2012/2013 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner