## MB152 Differential and Integral Calculus

**Faculty of Informatics**

Autumn 2023

**Extent and Intensity**- 2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).

Taught in person. **Teacher(s)**- doc. Mgr. Petr Hasil, Ph.D. (lecturer)

Mgr. Petr Liška, Ph.D. (seminar tutor)

Mgr. Matouš Trnka (seminar tutor)

Mgr. Gabriela Žárská (seminar tutor)

Mgr. Jiřina Šišoláková, Ph.D. (assistant)

doc. RNDr. Michal Veselý, Ph.D. (alternate examiner) **Guaranteed by**- doc. Mgr. Petr Hasil, Ph.D.

Department of Computer Science - Faculty of Informatics

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Prerequisites**- ( !
**MB202**Calculus B && !**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 53 fields of study the course is directly associated with, display
**Course objectives**- This is a basic course of the mathematical analysis. The content is the differential and integral calculus and the theory of infinite series. Students will understand theoretical and practical methods and will be able to apply these methods to concrete problems. The emphasis on theory and examples is balanced in the course.
**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;

analyse the behaviour of functions of one real variable.

understand the theory and use of infinite number series and power series;

understand the selected applications of the calculus;

apply the methods of the calculus to concrete problems. **Syllabus**- Continuous functions and limits
- Derivative and its applications
- Elementary functions
- Indefinite integral
- Riemann integral and its applications (including an introduction to basic differential equations)
- Introduction to differential (and integral) calculus of functions of several variables
- Infinite series

**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 - SLOVÁK, Jan, Martin PANÁK and Michal BULANT.
*Matematika drsně a svižně (Brisk Guide to Mathematics)*. 1st ed. 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

*recommended literature*- RILEY, K.F., M.P. HOBSON and S.J. BENCE.
**Teaching methods**- There are theoretical lectures and standard tutorial
**Assessment methods**- Two hours of lectures per week and two hours of exercises/seminar group. During the semester, there are 5 written tests in the seminar groups. The seminars are evaluated in total by max 10 points. Students, who collect during the semester (i.e., in exercises) less than 5 points, are graded as X and they do not proceed to the final examination. The final exam is a written test for max 35 points. For successful examination (the grade at least E), the student needs in total 20 points or more.
**Language of instruction**- Czech
**Further Comments**- The course is taught annually.

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

M2100 || FI:MB001||FI:MB102||M2B02||FI:MB202|| NOW(MIN301) || MIN301 || FI:MB152 **MB142**Applied math analysis

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

MB141 || MB142 || MB101 || MB201 || MB102 || MB202 || MB151 || MB152**MB153**Statistics I

( MB151 || MB101 || MB201 || MB152 || MB102 || MB202 || PřF:M1110 || PřF:M1100 ) && ( !MB103 && !MB203 && !MV011 )**MB154**Discrete mathematics

!MB104 && !MB204 && ( MB101 || MB201 || MB151 || MB102 || MB202 || MB152 || PřF:M1110 || PřF:M1100 )**PV291**Introduction to Digital Signal Processing

MB151&& MB152

- PřF:

- Enrolment Statistics (recent)

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