M4502 Mathematical Analysis 4

Faculty of Science
Spring 2019
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. Jaromír Šimša, CSc. (lecturer)
RNDr. Pavel Šišma, Dr. (seminar tutor)
Guaranteed by
prof. RNDr. Zuzana Došlá, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Wed 14:00–15:50 M5,01013
  • Timetable of Seminar Groups:
M4502/01: Mon 18. 2. to Fri 17. 5. Fri 12:00–13:50 M1,01017, P. Šišma
Prerequisites
Knowledge of the differential and integral calculus in one variable. 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
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of the course is to familiarize the student with the fundamental parts of the integral 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
  • Integral calculus of functions of several variables: double and triple integral on an interval and on a measurable set, Fubini's theorem, transformation of double and triple integrals, geometric applications of double and triple integrals. 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
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. 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, 2002, 453 pp. Matematická analýza s programem Maple, 2. ISBN 80-210-3005-4. Domovská stránka projektu Domovská stránka Díl 1. info
Bookmarks
https://is.muni.cz/ln/tag/PříF:M4502!
Teaching methods
Standard lecture with excersise to learn the computational skills.
Assessment methods
Examination: written and oral. Two written tests will be realized during the semester. It is required to obtain at least half of the total amount of points in each test. The exam is composed of a written and an oral part. The written part consists of four exercises. It is necessary to obtain at least 1,5 from possible 4 points.
Language of instruction
Czech
Follow-Up Courses
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, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020.
  • Enrolment Statistics (Spring 2019, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2019/M4502