M2B02 Calculus II

Faculty of Science
Spring 2015
Extent and Intensity
2/2. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Mgr. Milan Bačík (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
Tue 16:00–17:50 M1,01017
  • Timetable of Seminar Groups:
M2B02/01: Fri 10:00–11:50 M5,01013, M. Bačík
Prerequisites
Complete the course MB102.
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 continuation of the course MB102. It is devoted to the differential and integral calculus of functions of several variables and to function series. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to explain methods of proofs of the fundamental theorems; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyze selected problems from the topics of the course.
Syllabus
  • Functions of several variables
  • Limits and continuity for functions of several variables
  • Partial derivatives, directional derivatives, differential for functions of several variables
  • Local and global extrema for functions of several variables
  • Double integrals over rectangular sets
  • Double and triple integrals over measurable sets, the Fubini Theorem
  • Basic transformations for double and triple integrals
  • Integrals depending on parameter
  • Functional series
Literature
    recommended literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vydání první. Brno: Vydavatelství Masarykovy univerzity, 1994, 130 stran. ISBN 8021009926. 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, 1999, 80 pp. ISBN 80-210-2203-5. URL info
  • KUBEN, Jaromír, Šárka MAYEROVÁ, Pavlína RAČKOVÁ and Petra ŠARMANOVÁ. Diferenciální počet funkcí více proměnných. 2012. URL 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. 1. vyd. Brno: Masarykova univerzita, 2009, vi, 272. ISBN 9788021049758. 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
  • 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
Teaching methods
lectures (2 hours per week) and tutorials (2 hours per week)
Assessment methods
Exam consists of two main parts:
(i) written (a multiple-choice test with the theory + a practical part; it takes 120 minutes)
(ii) oral.
It is possible to get at most 100 points (25 points from the tutorial, 10 points from the test, 35 points from the practical part, and 30 points from the oral part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial, 4 points from the theory test and a nonzero number of points from the oral part.
Language of instruction
Czech
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 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019.
  • Enrolment Statistics (Spring 2015, recent)
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