M3501 Mathematical Analysis 3

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
2/2/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Jaromír Šimša, CSc. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
KREDITY_MIN(30)
Mathematical Analysis 1 (M1510), Mathematical Analysis 2 (M2510)
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 aim of the course is to familiarize the student with the elementary methods of the solution of the basic types of ordinary differential equations, with the fundamentals of the theory of metric spaces and with the introductory parts of differential calculus in more variables. After passing the course, the student will be able to solve selected types of ordinary differential equations and to understand and explain basic notions and techniques of the above-mentioned fields of mathematics including their mutual context.
Syllabus
  • Ordinary differential equations: elementary methods of solution of first order differential equations, higher order linear differential equations with constant coefficients. Metric spaces: metrics, convergence, closure, boundary and interior of a set, continuous mapping, compact set, Banach contraction principle. Differential calculcus of functions of several variables: limits, continuity, partial derivatives, differential.
Literature
  • RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 3. vyd. Brno: Masarykova univerzita, 2004, ii, 96. ISBN 8021034165. info
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 3., dopl. Praha: Academia, 1976, 669 s. URL 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. Vyd. 2. přeprac. Brno: Masarykova univerzita, 1999, iv, 143. ISBN 8021020520. info
  • PLCH, Roman, Zuzana DOŠLÁ and Petr SOJKA. Matematická analýza s programem Maple. Díl 1, Diferenciální počet funkcí více proměnných. (The Multivariable Calculus with program Maple. Part 1, Differencial calculus). prvni. Brno: Masarykova Universita, 1999, 80 pp. ISBN 80-210-2203-5. URL info
Teaching methods
Standard lectute and excersise in mathematical analysis.
Assessment methods
Teaching: lectures 2 hours a week, seminar 2 hours a week. Completion: credit written 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.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.