310-3142/01 – 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 introduction2019/2020Year 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

The mandatory participation is 80%.

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)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80 (80) 30
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation: The mandatory participation is 80%.

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2302R010) Design of Machines and Equipment (21) Design of Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2301R013) Robotics P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2019/2020 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2019/2020 (B0715A270011) Engineering (S04) Machine Design P Czech Ostrava 3 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner