MB202 Differential and Integral Calculus B

Faculty of Informatics
Spring 2019
Extent and Intensity
4/2. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Jakub Juránek (seminar tutor)
Supervisor
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
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 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.
Learning outcomes
At the end of the course students will be able to:
work both practically and theoretically with the derivative and (indefinite and definite) integral ;
use calculus for solving various applied problems;
analyse the behavior of functions of one real variable;
understand the theory and use of infinite number series and power series;
use some integral transforms and Fourier series.
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
  • SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1. vyd. Brno: Masarykova univerzita, 2013. 773 pp. ISBN 978-80-210-6307-5. doi:10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
  • 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
    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
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/spring2019/MB202

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