M2510 Mathematical Analysis 2

Faculty of Science
Spring 2011
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)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M2510/01: Thu 16:00–17:50 M6,01011, Z. Kadeřábek
M2510/02: Thu 18:00–19:50 M6,01011, Z. Kadeřábek
Prerequisites
Knowledge of the differential calculus in one variable is 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 main objective is to understand basic notions, results and techniques of computations and applications in the theory of integrals of one variable functions.
After passing the course, the student will be able:
to define and interpret the basic notions in theory of both definite and undefinite integrals:
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques of integratring one variable functions;
to apply acquired pieces of knowledge for the solution of specific problems, mainly in geometry and physics.
Syllabus
  • Sequences, differential of a function, Taylor's theorem. Primitive function. Basic integration methods. Integrals of rational, trigonometric and some irrational functions. Riemann definite integral and its geometric applications. Improper integrals.
Literature
  • Integrální počet. Edited by Vojtěch Jarník. Vyd. 5. nezměn. Praha: Academia, 1974, 243 s. URL info
  • NOVÁK, Vítězslav. Integrální počet v R. 2. vyd. Brno: Masarykova univerzita, 1994, 148 s. ISBN 8021009918. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : Riemannův integrál. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 84 s. info
  • Kuben, Jaromír - Hošková, Šárka - Račková, Pavlína. Integrální počet funkcí jedné proměnné; VŠB-TU Ostrava, elektronický text vytvořený v rámci projektu CZ.04.1.03/3.2.15.1/0016 ESF ČR. Dostupné z: http://homel.vsb.cz/~s1a64/cd/pdf/print/ip.pdf.
Teaching methods
Lectures and group-exercices.
Assessment methods
Two written tests. Exam in both oral and written form.
Language of instruction
Czech
Follow-Up Courses
Further Comments
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 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019.
  • Enrolment Statistics (Spring 2011, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2011/M2510