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

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

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 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%. To complete the credit, students must successfully pass the credit test. On the basis of a successfully completed credit, they can take an exam, which will consist of a practical and a theoretical part.

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Conditions for subject completion and attendance at the exercises within ISP: I order to complete the credit, students submit and defend a set of solved examples assigned by the teacher. On the basis of a successfully completed credit, they can take an exam, which will consist of a practical and a theoretical part.

Show history

Occurrence in study plans

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2022/2023 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
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2022/2023 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2021/2022 (B0715A270011) Engineering (S04) Machine Design P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2301R013) Robotics P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2302R010) Design of Machines and Equipment (21) Design of Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Design of industrial products P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2021/2022 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2020/2021 (B0715A270011) Engineering (S04) Machine Design P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2302R010) Design of Machines and Equipment (21) Design of Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Design of industrial products P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2303R002) Mechanical Engineering Technology P Czech Šumperk 3 Optional study plan
2020/2021 (B2341) Engineering (2301R013) Robotics P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
2020/2021 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
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) Design of industrial products 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

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