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PřF:M3100 Mathematical Analysis III - Course Information

## M3100 Mathematical Analysis III

**Faculty of Science**

autumn 2017

**Extent and Intensity**- 4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
**Teacher(s)**- doc. Mgr. Petr Hasil, Ph.D. (lecturer)

Mgr. Lenka Czudková, Ph.D. (seminar tutor)

Mgr. Peter Šepitka, Ph.D. (seminar tutor) **Guaranteed by**- doc. Mgr. Petr Hasil, Ph.D.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 18. 9. to Fri 15. 12. Mon 18:00–19:50 A,01026, Tue 11:00–12:50 A,01026
- Timetable of Seminar Groups:

*P. Šepitka*

M3100/51: Mon 18. 9. to Fri 15. 12. Thu 14:00–15:50 F3,03015,*L. Czudková* **Prerequisites**-
**M2100**Mathematical Analysis II

The knowledge from courses Mathematical Analysis I, II is assumed. **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**- Applied Mathematics for Multi-Branches Study (programme PřF, B-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)

**Course objectives**- The last part of the three semesters basic course of the mathematical analysis, devoted to infinite series and integral calculus of functions of several variables. After passing the course, the student will be able: to define and interpret the basic notions used in the basic parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in basic fields of analysis; to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
**Learning outcomes**- At the end of the course students will be able to:

define and interpret the notions from the theory of infinite series and integral calculus of functions of several variables;

formulate relevant mathematical theorems and to explain methods of their proofs;

analyse problems from the topics of the course;

understand to theoretical and practical methods of the theory of infinite series and integral calculus of functions of several variables;

apply the methods of mathematical analysis to concrete problems. **Syllabus**- I. Infinite number series: series with nonnegative summands, absolute and relative convergence, operations with infinite series. II. Infinite functional series: pointwise and uniform convergence, power series and their application, Fourier series. III. Integral calculus of functions of several variables: Jordan measure, Riemann integral, Fubini theorem, transformation theorem for multiple integrals, elements of curvelinear integral, integrals depending on a parameter.

**Literature**- DOŠLÁ, Zuzana and Vítězslav NOVÁK.
*Nekonečné řady*. Vyd. 1. Brno: Masarykova univerzita, 1998. 113 s. ISBN 8021019492. info - KALAS, Josef and Jaromír KUBEN.
*Integrální počet funkcí více proměnných (Integral calculus of functions of several variables)*. 1. vyd. Brno: Masarykova univerzita, 2009. 278 pp. ISBN 978-80-210-4975-8. info

*recommended literature*- RÁB, Miloš.
*Zobrazení a Riemannův integrál v En*. 1. vyd. Praha: Státní pedagogické nakladatelství, 1988. 97 s. info - JARNÍK, Vojtěch.
*Integrální počet (II)*. 2. vyd. Praha: Academia, 1976. 763 s. info - BUCK, R. Creighton.
*Advanced calculus*. 3d ed. Long Grove: Waveland Press, 2003. x, 622. ISBN 1577663020. info - ADAMS, R. A. and Christopher ESSEX.
*Calculus : a complete course*. 7th ed. Toronto: Pearson, 2010. xvi, 973. ISBN 9780321549280. info - BRAND, Louis.
*Advanced calculus : an introduction to classical analysis*. New York: John Wiley & Sons, 1955. 574 s. info

*not specified*- DOŠLÁ, Zuzana and Vítězslav NOVÁK.
**Teaching methods**- Standard theoretical lectures with excercises.
**Assessment methods**- Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.

3 written intrasemestral tests in seminars (30% of the overall evaluations).

Final exam: Written test (40%) and oral exam (30%).

To pass: at least 1/3 points from intrasemestral tests, then 45% in total.

Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester. **Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses**

- Enrolment Statistics (autumn 2017, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2017/M3100