MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2015
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Eva Janoušková, Ph.D. (seminar tutor)
Mgr. Marek Sas (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Fri 8:00–11:50 A217
  • Timetable of Seminar Groups:
MB202/T01: Mon 16. 2. to Fri 15. 5. Mon 9:40–11:15 116, E. Janoušková, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB202/01: Mon 8:00–9:50 A320, M. Sas
MB202/02: Mon 10:00–11:50 A320, M. Sas
Prerequisites
!NOW( MB102 Calculus ) && ! MB102 Calculus
High school mathematics.
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 16 fields of study the course is directly associated with, display
Course objectives
The second part of the block of four courses in Mathematics in its extended version. In the whole course, the fundamentals of general algebra, linear algebra and mathematical analysis, including their applications in probability, statistics are presented. This semester is concerned with the basic concepts of Calculus including numerical and applied aspects. The students will be able to work both practically and theoretically with the derivative and integral (indefinite and definite intergral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable. Students will understand the theory and use of infinite number series and power series, they will also learn about applications of some integral transforms.
Syllabus
  • 1. Creating the ZOO (4 weeks) – interpolation of data by polynomials and splines; axiomatics of real numbers; topology of real numbers; scalar sequences,limits of sequenses and functions; continuity and derivatives; introduction of elementary functions via continuity; power series and goniometric functions;
  • 2. Differential and integral Calculus (5 weeks) – higher order derivatives and Taylor expansion; extremes of functions; Riemann and Newton integration (area, volumes, etc.); uniform convergence and their consequences; Laurant series in complex variable; numerical derivatives and integration; stronger integration concepts (Riemann-Stieltjes, Kurzweil)
  • 3. Continuous models (3 week) – aproximation of functions via orthogonal systems; Fourier series (including the numerical aspects); integral transforms, discrete Fourier transform
Literature
    recommended literature
  • RILEY, K.F., M.P. HOBSON and S.J. BENCE. Mathematical Methods for Physics and Engineering. second edition. Cambridge: Cambridge University Press, 2004, 1232 pp. ISBN 0 521 89067 5. info
  • Matematická analýza pro fyziky. Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001, v, 320 s. ISBN 80-85863-65-0. info
  • J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
Teaching methods
Lecture combining theory with problem solving. Seminar groups devoted to solving problems.
Assessment methods
Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
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 2013, Spring 2014, Spring 2016, Spring 2017, Spring 2018, Spring 2019.
  • Enrolment Statistics (Spring 2015, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2015/MB202