714-0324/02 – Matrix analysis and variational calculus (MVA)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits2
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year3Semestersummer
Study languageCzech
Year of introduction2004/2005Year of cancellation2009/2010
Intended for the facultiesFSIntended for study typesBachelor
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
Combined Credit and Examination 12+4

Subject aims expressed by acquired skills and competences

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

Teaching methods

Lectures
Tutorials

Summary

The course deals with the matrix calculus and the variational calculus in the context of engineering problems. The course ends by the algorithmization of the finite element method.

Compulsory literature:

1. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999, ISBN-13: 9780139491573. 2. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007, ISBN: 978-3-540-34658-6. 3. Golub G.H., Loan C.F.V.: Matrix Computation. The Johns Hopkins University Press, Baltimore, 1996, ISBN 0-8018-5414-8.

Recommended literature:

1. A. Tveito, R. Winther: Introduction to Partial Differential Equations: A Computational Approach. Springer, Berlin, 2000. 2. http://mi21.vsb.cz/

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1 Vektorový prostor, lineární zobrazení a matice. 2 Skalární součin a ortogonalita, ortogonalizační proces. 3 Vlastní čísla a vektory, spektrální rozklad. 4 Singulární čísla a singulární rozklad. Zobecněná inverze. 5 Speciální maticové rozklady a jejich použití. Rychlé řešení soustav lineárních rovnic. 6 Gradientní metody řešení soustav lineárních rovnic. Předpodmínění. 7 Lineární, bilineární a kvadratické formy a jejich klasifikace. 8 Slabá řešení diferenciálních rovnic. 9 Věty o existenci slabých řešení. 10 Variační metody řešení diferenciálních rovnic, Ritzova a Galerkinova metoda. 11 Úvod do metody konečných prvků. 12 Numerické příklady I: okrajové úlohy pro obyčejné diferenciální rovnice. 13 Numerické příklady II: okrajové úlohy pro parciální diferenciální rovnice. 14 Základy tenzorového počtu.

Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester, validity until: 2009/2010 Summer 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 20 (20) 0
                Project Project 5  0
                Written exam Written test 15  0
        Examination Examination 80 (80) 0
                Written examination Written examination 60  0
                Oral Oral examination 20  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment K Czech Šumperk 3 Optional study plan
2009/2010 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R007) Hydraulics and Pneumatics K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (3907R004) Energy Management K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2301R013) Robotics (70) Robotics K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Šumperk 3 Optional study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport K Czech Ostrava 3 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Šumperk 3 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Ostrava 3 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Uherský Brod 3 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Třinec 3 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Šumperk 3 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Ostrava 3 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Uherský Brod 3 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Třinec 3 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Šumperk 3 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Ostrava 3 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Uherský Brod 3 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Třinec 3 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Šumperk 3 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Ostrava 3 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Uherský Brod 3 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty K Czech Třinec 3 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner