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Mathematical analysis III

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-2422/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KRC76Mgr. Jiří Krček
SWA0013RNDr. Martin Swaczyna, Ph.D.
Summary
This subject presents the part of basic mathematical course in the bachelor degree.
Learning Outcomes of the Course Unit
This subject offers basic knowledges of vector analysis related to mathematical physics.
The main goals are oriented to
- fundamental knowledges of mathematical analysis of vectorial functions,
- an use of differential operators in application problems,
- the appropriating of computational methods for curvilinear and surface integrals,
- an overview of main field theory aspects with relation to the solving of PDE.
Course Contents
1. Scalar and vector fields.
2. Differential operators.
3. Local characteristics of vector fields.
4. Curvilinear integrals.
5. Surface integrals.
6. Global characteristics of vector fields.
7. Introduction to the potential theory.
8. Integral representation of solution of several second-order PDE.
Recommended or Required Reading
Required Reading:
MEJLBRO, L. Calculus 2b – Real Functions in Several Variables. http://bookboon.com/cs/calculus-2b-3-ebook. ISBN 87-7681-206-5.
[1] BOUCHALA, J. Matematická analýza 3. Ostrava: VŠB – Technická univerzita Ostrava, 2001. studijní text.
[2] BOUCHALA, J., VLACH, O. Křivkový a plošný integrál. Ostrava: VŠB – Technická univerzita Ostrava, 2012. http://mi21.vsb.cz/modul/krivkovy-plosny-integral .
[3] http://mdg.vsb.cz/M/index.php?e=0,83 (studijní materiály Katedry matematiky a deskr. geometrie)
Recommended Reading:
SPIEGEL, R. M., LIPSCHUTZ, S., SPELLMAN, D. Vector Analysis, 2nd edition, McGraw-Hill, 2009, ISBN 978-7161-545-7
[1] REKTORYS, K. et al. Přehled užité matematiky I, II. 7. vyd. Praha: Prometheus, 2009. ISBN 978-80-7196-180-2.
[2] BRABEC, J., HRŮZA, B. Matematická analýza II. Praha: SNTL, 1986.
[3] BUDÍNSKÝ, B., CHARVÁT, J. Matematika II, Praha: SNTL, 1990.
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 15
        ExaminationExamination70 21