PřF:M2050 Diff. calc. and diff. equat.

M2050 Differential calculus of several variables and differential equations

Faculty of Science
Spring 2000

Extent and Intensity

4/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)

Guaranteed by

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

Syllabus

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 2001.