M2050 Differential calculus of several variables and differential equations

Faculty of Science
Spring 2001
Extent and Intensity
4/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zuzana Došlá, DSc. (lecturer), Mgr. Viktor Votruba, Ph.D. (deputy)
Mgr. Tomáš Radlička, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Zuzana Došlá, DSc.
Departments – Faculty of Science
Contact Person: prof. RNDr. Zdeněk Pospíšil, Dr.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Metric Spaces -- Basic concepts and properties of metric spaces, spaces $\Bbb E^n$. -- Cauchy and convergent sequences, complete spaces. -- Banach fixed point theorem and its applications. -- Continuous mappings of compact spaces. Differential Calculus of Functions of Two or More variables -- Notion of a function of two or more variables, limits, continuity (on the base of metrix spaces). -- Partial derivatives and differentiability. -- Taylor theorem. -- Local and absolute extrema. -- Implicit functions. Differential Equations -- First order differential equations, the existence--uniqueness theorem. -- Elementary methods for solving first order diferential equations and applications. -- Second order linear differential equations with constant coefficients. Infinite series of numbers: convergence, absolute and nonabsolute convergence, basic tests for convergence, operations with series. Calculus of variations: basic concepts.
Literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Metrické prostory : teorie a příklady. 1. dotisk 2. přeprac. vyd. Brno: Masarykova univerzita, 2000, [iii], 83. ISBN 8021013281. info
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vydání první. Brno: Vydavatelství Masarykovy univerzity, 1994, 130 stran. ISBN 8021009926. info
  • RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 2. přeprac. vyd. Brno: Masarykova univerzita, 1998, 96 s. ISBN 8021018186. info
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : nekonečné řady. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1992, 76 s. ISBN 8021003855. info
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 3., dopl. Praha: Academia, 1976, 669 s. URL info
  • PLCH, Roman. Příklady z matematické analýzy : Diferenciální rovnice. Brno: Masarykova univerzita, 1995, 29 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2000.
  • Enrolment Statistics (recent)
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