M4502 Mathematical Analysis 4

Faculty of Science
Spring 2012
Extent and Intensity
2/2/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Mgr. Zdeněk Kadeřábek, Ph.D. (seminar tutor)
Mgr. Silvie Šabacká (assistant)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M4502/01: Mon 17:00–18:50 M3,01023, Z. Kadeřábek
Prerequisites
Knowledge of the differential and integral calculus in one variable and basic knowledge on metric spaces. Acquaintance with the limit, continuity, partial derivatives and the differential of the functions in more variables.
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
The aim of the course is to familiarize the student with the fundamental parts of the differential calculus in more variables, with infinite number series and with sequences and series of functions. After passing the course, the student will be able to understand rudiments of the above-mentioned fields of mathematics and to explain basic notions and techniques and their mutual context.
Syllabus
  • Differential calculus of functions of several variables: Taylor theorem, extremes of functions, implicit functions. Infinite number series: sum of series, operations with series, convergence criteria, absolute convergence. Sequences and series of functions: uniform convergence, integration and derivation of series, power series, Taylor series.
Literature
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 3., dopl. Praha: Academia. 669 s. 1976. URL info
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vyd. 2. přeprac. Brno: Masarykova univerzita. iv, 143. ISBN 8021020520. 1999. info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita. 113 s. ISBN 8021019492. 1998. info
  • DOŠLÁ, Zuzana, Roman PLCH and Petr SOJKA. Matematická analýza s programem Maple. Díl 2, Nekonečné řady. (The Multivariable Calculus with program Maple. Part 2, Infinite series.). prvni. Brno: Masarykova univerzita. 453 pp. Matematická analýza s programem Maple, 2. ISBN 80-210-3005-4. 2002. Domovská stránka projektu Domovská stránka Díl 1. info
  • PLCH, Roman, Zuzana DOŠLÁ and Petr SOJKA. Matematická analýza s programem Maple. Díl 1, Diferenciální počet funkcí více proměnných. (The Multivariable Calculus with program Maple. Part 1, Differencial calculus). prvni. Brno: Masarykova Universita. 80 pp. ISBN 80-210-2203-5. 1999. URL info
Bookmarks
https://is.muni.cz/ln/tag/PříF:M4502!
Teaching methods
Written and oral exam.
Assessment methods
Teaching: lectures 2 hours a week, seminar 2 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020.
  • Enrolment Statistics (Spring 2012, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2012/M4502