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)
prof. Mgr. Petr Hasil, Ph.D. (lecturer)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
Guaranteed by
prof. 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:
M3100/01: Mon 18. 9. to Fri 15. 12. Wed 18:00–19:50 M1,01017, 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
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
    recommended 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). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
    not specified
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL 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, x, 574. info
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
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (autumn 2017, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2017/M3100