M4140 Selected Topics in Mathematical Analysis

Faculty of Science
Spring 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)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Ilja Kossovskij, Ph.D. (lecturer)
doc. Mgr. Peter Šepitka, Ph.D. (seminar tutor)
doc. RNDr. Martin Kolář, Ph.D. (alternate examiner)
Guaranteed by
prof. RNDr. Zuzana Došlá, 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 14:00–15:50 M6,01011, Thu 16:00–17:50 M3,01023
  • Timetable of Seminar Groups:
M4140/01: Mon 18. 2. to Fri 17. 5. Thu 18:00–19:50 M3,01023, P. Šepitka
Prerequisites
M3100 Mathematical Analysis III
Mathematical analysis: differential and integral calculus of functions one and more variables.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is a continuation of the basic courses of the mathematical analysis and extends them for needs of applied disciplines. It is dedicated to students who do not attend special courses of ordinary differential equations, the complex analysis, and the linear functional analysis. After passing the course, the student will be able: to define and interpret the basic notions used in the corresponding parts of mathematical analysis and to explain their mutual context; to formulate relevant mathematical theorems and statements; 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 ordinary differential equations, the complex analysis, and the linear functional analysis; formulate relevant mathematical theorems; analyse problems from the topics of the course; use effective techniques utilized in basic fields of analysis; apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  • Ordinary differential equations: differential equations of first order, systems of linear differential equations, linear differential equations of n-th order, systems of nonlinear differential equations, local and global properties of solution, autonomous systems, introduction to theory of stability.
  • Elements of the complex analysis: limit and continuity for function of complex variable, infinite series in complex domain, elementary function in complex domain, derivative of function of complex variable, holomorphic functions and their properties, line integral in complex plain, Cauchy theorem, Taylor series, Laurent series, isolated singularities, residue theorem.
  • Elements of the linear functional analysis: inner product spaces, Fourier series, bounded linear operators, compact operators.
Literature
  • RÁB, Miloš. Diferenciální rovnice. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1980, 196 s. URL info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. info
  • Novák,Vítězslav.Analýza v komplexním oboru.1.vyd.Praha:Státní pedagogické nakladatelství,1984,103 s..
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
Teaching methods
theoretical preparation, exercise
Assessment methods
Two written tests during the semester, consisting of 10 questions each. 50% of total points is needed to pass. Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
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 2020.
  • Enrolment Statistics (Spring 2019, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2019/M4140