M7240 Selected topics in classical mathematical analysis

Faculty of Science
Autumn 2008
Extent and Intensity
0/2. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: k (colloquium). Other types of completion: zk (examination).
Teacher(s)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 14:00–15:50 MS2,01022
Prerequisites
M1100 Mathematical Analysis I && M2100 Mathematical Analysis II && M3100 Mathematical Analysis III
Differential and integral calculus of functions of one and several variables, infinite series. Recommended (but not obligatory) prerequisity is the knowledge of linear functional analysis (M6150, resp. M7180).
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
This course contains additional/extending topics from mathematical analysis. The aim is to offer advanced topics which the students will study and, after consultations with the teacher, present to other students in the class. Therefore, the students will also prepare and give their own presentation/lecture.
Syllabus
  • The content of this course are supplementary topics in mathematical analysis, such as (examples) - locally convex topological vector spaces, - elements of the theory of distributions, - summation of divergent series, - infinite products, - functional equations and elementary functions, - Gamma and Beta functions, their properties and applications, - elliptic integrals, - uniform continuity, - iterations, cycles, and chaos, - basic calculus on time scales.
Literature
  • BOHNER, Martin and Allan PETERSON. Dynamic Equations on Time Scales. An Introduction with Applications. Boston, MA: Birkhauser, 2001. ISBN 0-8176-4225-0. info
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 3., dopl. Praha: Academia, 1976, 669 s. URL info
  • JARNÍK, Vojtěch. Integrální počet. Vyd. 2. Praha: Academia, 1976, 763 s. URL info
Assessment methods
Students will present an hour (two hour) lecture on a given topic (for colloquium). Optionally, there can be a final exam.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 2004, Autumn 2006.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2008/M7240