714-0324/01 – 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 cancellation
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
Full-time Credit and Examination 2+2

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

Tests and credits ================= Exercises --------- Conditions for obtaining credit points (CP): - participation in exercises, 20% can be to apologize - completion of three written tests, 0-15 CP - completion of two programs, 5 CP Exam ---- - written exam 0-60 CP, successful completion at least 25 CP - oral exam 0-20 CP, successful completion at least 5 CP The exam questions are analogous to the program of the lectures.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Week. Lecture ------------- 1st Vector space, linear mappings and matricies. 2nd Scalar product and orthogonality, orthogonalization procedure. 3rd Eigenvalues and eigenvectors, spectral decomposition. 4th Singular values and singular decomposition. Generalized inverse. 5th Matrix factorizations. Fast solving of linear systems. 6th Gradient descent method. Preconditioning. 7th Linear, bilinear and quadratic forms. Classification. 8th Weak solutions of differential equations. 9th Theorems on existence of weak solutions. 10th Variational solving differential equations. Ritz-Galerkin method. 11th Fundamentals of the finite element method. 12th Model boundary value problems for ODEs. 13th Model boundary value problems for PDEs. 14th Comparision with the finite difference method.

Conditions for subject completion

Full-time form (validity from: 2010/2011 Summer semester, validity until: 2013/2014 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 20 (20) 5
                Project Other task type 5  5
                Written exam Written test 15  0
        Examination Examination 80 (80) 30
                Written examination Written examination 60  25
                Oral Oral examination 20  5
Mandatory attendence parzicipation:

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2018/2019 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2018/2019 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
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2017/2018 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
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2016/2017 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
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2016/2017 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
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2015/2016 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2301R013) Robotics P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2015/2016 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
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2015/2016 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
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2015/2016 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2302R010) Design of Machines and Equipment (21) Design of Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
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2014/2015 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2302R010) Design of Machines and Equipment (21) Design of Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
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2014/2015 (B2341) Engineering (2301R013) Robotics P Czech Ostrava 3 Optional study plan
2014/2015 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (2301R013) Robotics P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2013/2014 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
2013/2014 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Optional study plan
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2013/2014 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
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2012/2013 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2301R013) Robotics P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2012/2013 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
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2012/2013 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
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2011/2012 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
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2011/2012 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2011/2012 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Optional study plan
2010/2011 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
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2010/2011 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Optional study plan
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2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
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2010/2011 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Optional study plan
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2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (20) Surface Transport P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment P Czech Šumperk 3 Optional study plan
2009/2010 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Optional study plan
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2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 3 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 3 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 3 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 3 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 3 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 3 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 3 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 3 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner