## MB102 Differential and Integral Calculus

**Faculty of Informatics**

Spring 2017

**Extent and Intensity**- 2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
**Teacher(s)**- doc. Mgr. Petr Hasil, Ph.D. (lecturer)

Mgr. Milan Bačík (seminar tutor)

Mgr. Pavel Francírek, Ph.D. (seminar tutor)

Mgr. Jan Hrdlička (seminar tutor)

Mgr. Jan Jekl (seminar tutor)

Mgr. Jakub Juránek (seminar tutor)

Mgr. Lukáš Másilko (seminar tutor)

Mgr. Mária Šimková (seminar tutor)

doc. RNDr. Michal Veselý, Ph.D. (alternate examiner) **Guaranteed by**- prof. RNDr. Jan Slovák, DrSc.

Faculty of Informatics

Supplier department: Faculty of Science **Timetable**- Mon 20. 2. to Sun 14. 5. Wed 12:00–13:50 D1, Wed 12:00–13:50 D3; and Wed 17. 5. 12:00–13:50 D2
- Timetable of Seminar Groups:

*L. Másilko*, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.

MB102/01: Tue 12:00–13:50 B204,*P. Hasil*

MB102/02: Tue 14:00–15:50 B204,*P. Hasil*

MB102/03: Tue 16:00–17:50 B204,*J. Hrdlička*

MB102/04: Tue 18:00–19:50 B204,*J. Hrdlička*

MB102/05: Thu 16:00–17:50 B204,*J. Juránek*

MB102/06: Thu 18:00–19:50 B204,*J. Juránek*

MB102/07: Wed 18:00–19:50 B204,*J. Juránek*

MB102/08: Tue 8:00–9:50 A320,*P. Francírek*

MB102/09: Tue 10:00–11:50 A320,*P. Francírek*

MB102/10: Fri 10:00–11:50 A320,*M. Bačík*

MB102/11: Fri 12:00–13:50 A320,*M. Bačík*

MB102/12: Tue 16:00–17:50 A320,*M. Šimková*

MB102/13: Tue 18:00–19:50 A320,*J. Jekl*

MB102/14: Wed 18:00–19:50 A320,*J. Hrdlička*

MB102/15: Wed 10:00–11:50 A320,*M. Veselý* **Prerequisites**- ! NOW (
**MB202**Calculus B ) && !**MB202**Calculus B

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 students will be able:

to work both practically and theoretically with the derivative and integral (indefinite and definite integral) and use them for solving various applied problems and for the analysis of behavior of functions of one real variable

understand the theory and use of infinite number series and power series, and they will meet selected applications of the Calculus. **Syllabus**- The course is the second part of the four semester block of Mathematics. The course Differential and Integral Calculus, in particular, is concerned with the basic concepts of Calculus including numerical and applied aspects.
- Polynomial interpolation, derivative of polynomials, cubic splines
- Continuous functions and limits
- Derivative and its applications
- Elementary functions
- Indefinite integral
- Riemann integral and its applications
- Infinite series and power series, Fourier series, integral transformations

**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 *Matematická analýza pro fyziky.*Edited by Pavel Čihák. Vyd. 1. Praha: Matfyzpress, 2001. v, 320 s. ISBN 80-85863-65-0. 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

*recommended literature*- DOŠLÁ, Zuzana and Vítězslav NOVÁK.
*Nekonečné řady*. Vyd. 1. Brno: Masarykova univerzita, 1998. 113 s. ISBN 8021019492. info

*not specified*- SLOVÁK, Jan, Martin PANÁK and Michal BULANT.
**Bookmarks**- https://is.muni.cz/ln/tag/FI:MB102!
**Teaching methods**- There are theoretical lectures and standard tutorial accompanied by homework assessment.
**Assessment methods**- Two hours of lectures per week and two hours of compulsory exercises/seminar group. During the semester, two obligatory mid-term exams are avaluated (each for max 10 points). In the seminar groups there are 4-6 half an hour exams during the semester. The seminars are evaluated in total by max 5 points. Students, who collect during the semester (i.e., in exercises and mid-term exams) less than 10 points, are graded as F and they do not proceed to the final examination. The final exam is two hours long and written for max 20 points. For successfull examination (the grade at least E) the student needs in total 20 points or more.
**Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

The course is taught each semester. **Listed among pre-requisites of other courses**- PřF:
**M3121**Probability and Statistics I

M2100 || FI:MB001||FI:MB102||M2B02||FI:MB202|| NOW(MIN301) || MIN301 **MA015**Graph Algorithms

MB005||(MB101&&MB102)||(MB201&&MB102)||(MB101&&MB202)||(MB201&&MB202)||(PřF:M1120)||PROGRAM(N-IN)||PROGRAM(N-AP)**MB142**Applied math analysis

!MB152 && !NOW(MB152) && !MB102 && !MB202**MB143**Design and analysis of statistical experiments

MB141 || MB142 || MB101 || MB201 || MB102 || MB202**MB152**Differential and Integral Calculus

( !MB202 && !MB102 )**MB153**Statistics I

( MB151 || MB101 || MB201 || MB152 || MB102 || MB202 ) && ( !MB103 && !MB203 && !MV011 )**MB154**Discrete mathematics

!MB104 && !MB204 && ( MB101 || MB201 || MB151 || MB102 || MB202 || MB152 )

- PřF:

- Enrolment Statistics (Spring 2017, recent)
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