M3100 Mathematical Analysis III

Faculty of Science
Autumn 2014
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
RNDr. Iva Dřímalová, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 10:00–11:50 M1,01017, Tue 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M3100/01: Tue 8:00–9:50 M4,01024, I. Dřímalová
M3100/02: Wed 14:00–15:50 M3,01023, P. Šepitka
M3100/03: Wed 8:00–9:50 M3,01023, P. Šepitka
M3100/51: Wed 10:00–11:50 F4,03017
Prerequisites
M2100 Mathematical Analysis II
The courses Mathematical Analysis I,II are supposed.
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 last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.
Literature
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • 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
Teaching methods
theoretical preparation, exercise
Assessment methods
Standard lecture and accompanying seminar, the final exam consists of written test and oral exam. The form of this final exam is the same as for previous courses Mathematical Analysis I,II
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 Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2014, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2014/M3100