M2100 Mathematical Analysis II

Faculty of Science
Spring 2025
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
Mgr. Jan Jekl, Ph.D. (seminar tutor)
Mgr. Ludmila Linhartová (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
Prerequisites
M1100 Mathematical Analysis I || M1101 Mathematical Analysis I || M1100F Mathematical Analysis I
Differential and integral calculus of functions of one variable, i.e., the course Mathematical Analysis I.
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
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.
Learning outcomes
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. 1. dotisk 2. přeprac. vyd. 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
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week. Seminars are evaluated up to 5 points. To be eligible for the exam, the student needs at least 1 point from the seminar.
Final exam: Written and oral part, all personal attendance, in total 20 points, from which 10 points are for theoretical part.
To pass: at least 50% points (i.e., 12.5 points) out of 25 points.
The conditions for final evaluation may be specified later depending on the pandemic situation and legal regulations.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2025/M2100