PMZM3 Introduction to mathematics III

Faculty of Economics and Administration
Autumn 2008
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Vítězslav Veselý, CSc. (lecturer)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Vítězslav Veselý, CSc.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Timetable
Fri 7:40–9:15 P304
  • Timetable of Seminar Groups:
PMZM3/1: Tue 7:40–9:15 P303, M. Matulová
Prerequisites
PMZMII Introduction to Mathematics II
The course is the last part of a three-semester family of courses "Introduction to mathematics I-III" within the BSc study program Economic Information systems (EIS).
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 20 student(s).
Current registration and enrolment status: enrolled: 0/20, only registered: 0/20, only registered with preference (fields directly associated with the programme): 0/20
Course objectives
The course is the last part of a three-semester family of courses "Introduction to mathematics I-III" primarily intended for BSc students of Economic Information systems (EIS).
Its main purpose is to make the students familiar with basic mathematical disciplines at introductory level so that they will be able to understand and actively apply exact mathematical tools in economic problem solving tasks.
The main topics of this final part are:
- basics of differential and integral calculus for functions of two or more variables
- convergence of functional sequences
- summation of functional series
- basics of Fourier analysis
- optional topics according to the the needs of successive courses
Syllabus
  • BIVARIATE AND MULTIVARIATE DIFFERENTIAL AND INTEGRAL CALCULUS: -Methods of graphical visualization, examples using MATLAB. -Limits and continuity. Partial derivatives. Total differential. Taylor's theorem. -Local and constrained extremes of bivariate and multivariate functions (local and global) and their applications. -Multivariate Riemann integral: definition, Fubini's theorem, transformation of the integration domain. FUNCTIONAL SEQUENCES AND SERIES: - Functional sequences, types of convergence. - Functional series, power series, convergence radius. - Fourier series, convergence, Parseval identity, discrete Fourier transform. SPECIAL TOPICS (specified at the lecture in more detail)
Literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vydání první. Brno: Vydavatelství Masarykovy univerzity, 1994, 130 stran. ISBN 8021009926. 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
  • DOŠLÁ, Zuzana, Roman PLCH and Petr SOJKA. Matematická analýza s programem Maple. Díl 2, Nekonečné řady. (The Multivariable Calculus with program Maple. Part 2, Infinite series.). prvni. Brno: Masarykova univerzita, 2002, 453 pp. Matematická analýza s programem Maple, 2. ISBN 80-210-3005-4. Domovská stránka projektu Domovská stránka Díl 1. info
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). Prvni dotisk 1. vyd. Brno: Masarykova univerzita v Brně, 2002, 120 pp. skripta. ISBN 80-210-1949-2. info
  • RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 2.přepracované vydání. Brno: vydala Masarykova univerzita v Brně-PřF, 1998, 96 pp. ISBN 80-210-1818-6. info
  • PLCH, Roman. Příklady z matematické analýzy : Diferenciální rovnice. Brno: Masarykova univerzita, 1995, 29 s. info
  • TU, Pierre N. V. Dynamical systems : an introduction with applications in economics and biology. 2nd rev. and enl. ed. Berlin: Springer-Verlag, 1994, xviii, 314. ISBN 3540576614. info
  • MINORSKIJ, Vasilij Pavlovič. Sbírka úloh z vyšší matematiky. Vyd. druhé nezměněné. Praha: SNTL, 1964, 298 s. info
Assessment methods
The course has a form of a lecture (2 lessons) accompanied by compulsory tutorials. The course is concluded by an oral exam provided that the student attended the tutorials regularly and successfully passed all intermediate written tests. He or she must prove understanding of basic theoretical concepts and the ability to solve practical sample problems. The final grade is a combined result of point evaluation obtained at the oral exam and written tests.
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 Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/econ/autumn2008/PMZM3