PřF:M2100 Mathematical Analysis II - Course Information
M2100 Mathematical Analysis II
Faculty of ScienceSpring 2019
- Extent and Intensity
- 4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
Mgr. Jakub Juránek, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 18. 2. to Fri 17. 5. Tue 10:00–11:50 M1,01017, Thu 12:00–13:50 M1,01017
- Timetable of Seminar Groups:
M2100/02: Mon 18. 2. to Fri 17. 5. Mon 14:00–15:50 M1,01017, J. Jekl
M2100/03: Mon 18. 2. to Fri 17. 5. Tue 12:00–13:50 M4,01024, J. Jekl - Prerequisites
- ( M1100 Mathematical Analysis I || M1101 Mathematical Analysis I ) && ! M2100F Mathematical Analysis II && !OBOR(UM) && !OBOR(FYZ) && !OBOR(NAN) && !OBOR(ASTR)
Differential and integral calculus of functuions of one variable, i.e. the couse Mathematical Analysis I (M1100). - 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
- Second part of the basic course of the mathematical analysis. The subject of the course are elementary methods of solution of differential equations, then the theory of metric spaces and finally the diferential 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.
- Syllabus
- I. Elementary methods of solution of differential equations: methods for first order equations, higher order linear differential equations with constant coefficients, systems of linear differential equations. II. Metric spaces: basic definitions, convergence, open and closed sets, continuous mappings, complete spaces, compact spaces, Banach contraction principle. III. Differential calculus of functions of several variables: limit, continuity, partial derivatives, Taylor's formula, extrema, mappings between higherdimensional spaces, implicit function theorem, constrained extrema.
- Literature
- recommended literature
- RÁB, Miloš. Metody řešení diferenciálních rovnic. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1989, 68 s. info
- DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Metrické prostory : teorie a příklady. 2. přeprac. vyd., Dotisk se. Brno: Masarykova univerzita, 2000, [iii], 83. ISBN 8021013281. info
- DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vydání první. Brno: Vydavatelství Masarykovy univerzity, 1994, 130 stran. ISBN 8021009926. info
- Sbírka řešených příkladů z matematické analýzy II (odkaz v učebních materiálech) https://is.muni.cz/auth/publication/1364246/cs?lang=cs
- Teaching methods
- Theoretical lecture with seminar.
- Assessment methods
- Final exam consists of written test and oral exam. Results of the intrasemestral tests are included in the overall evaluation. There will be 3(+1) written intrasemestral tests in tutorials.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually. - Listed among pre-requisites of other courses
- F3063 Integration of forms
(M1100&&M2100)||(M1100F&&M2100F) - M3100 Mathematical Analysis III
M2100 - M3100F Mathematical Analysis III
( M2100F || M2100 ) && !M3100 - M3121 Probability and Statistics I
M2100 || FI:MB001||FI:MB102||M2B02||FI:MB202|| NOW(MIN301) || MIN301 || FI:MB152
- F3063 Integration of forms
- Enrolment Statistics (Spring 2019, recent)
- Permalink: https://is.muni.cz/course/sci/spring2019/M2100