M4140 Selected Topics in Mathematical Analysis

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

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. Miroslav Bartušek, DrSc. (lecturer)
doc. RNDr. Martin Kolář, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M3100 Mathematical Analysis III
Mathematical analysis:Differential and integral calculus of functions one and more variables.
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 discipline continues the basic course of the mathematical analysis and extends it for needs of applied disciplines.It is dedicated to students which do not study special courses of ordinary differential equations, the linear functional analysis and the complex analysis . 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; 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
  • Ordinary differential equations:Cauchy initial value problem,local and global solutions,an introduction to the stability theory,autonomous equations, differential inequalities, basic properties of second order linear differential equations. Elements of the complex analysis:holomerphic functions,Cauchy theorem, Taylor series,Laurent series,isolated singularities,residua theory and its applications in computing improper integrals. Elements of the linear functional analysis:Spaces with the inner product,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..
Teaching methods
theoretical preparation,exercise
Assessment methods
Standard lecture and exercise finished by oral exam.
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.
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 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020.