310-3142/02 – 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 languageEnglish
Year of introduction2019/2020Year of cancellation2021/2022
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

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.

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

Other requirements

Credits are awarded on submission of all properly drafted tasks and active participation in exercises. The condition of the test are credits. Part of the test is oral with written preparation.

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: 2019/2020 Winter semester, validity until: 2021/2022 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80 (80) 30 3
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence participation: The mandatory participation is 80%.

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

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (B2341) Engineering (3902R001) Applied Informatics and Control P English Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (3907R009) Operation of Energy Equipment P English Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2303R002) Mechanical Engineering Technology P English Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2301R013) Robotics P English Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (3901R003) Applied Mechanics P English Ostrava 3 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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