MUC13 Mathematical Analysis 3

Faculty of Science
Autumn 2019
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Jaromír Šimša, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: 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 basic parts of differential calculus in more variables, with the elementary methods of solving the basic types of ordinary differential equations and with the basic parts of power series. After passing the course, the student will be able to solve extremal problems for functions in more variables, selected types of ordinary differential equations and to use the integration and derivation of power series. The student will be able to understand and explain basic notions and techniques of the above-mentioned fields of mathematics including their mutual context.
Learning outcomes
After passing the course, the student will be able:
to understand the differential calculus of functions in more variables (the notation of function, limit, continuability, partial derivatives, local and global extremes);
to solve the basic ordinary differential equations of the first and second order;
to know the theory of power series (convergence radius, derivation and integration of series, the expansion of functions to power series).
Syllabus
  • Differential calculcus of functions of several variables: limits, continuity, partial derivatives, differential, Taylor theorem, local and absolute extrema of functions, implicit function.
  • Ordinary differential equations: elementary methods of solution of first order differential equations, higher order linear differential equations with constant coefficients.
  • Power series - convergence radius and interval, derivation and integration of series, the expansion of functions to power series.
Literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vyd. 2. přeprac. Brno: Masarykova univerzita, 1999, iv, 143. ISBN 8021020520. info
  • RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 3. vyd. Brno: Masarykova univerzita, 2004, ii, 96. ISBN 8021034165. info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady (Infinite series). 2nd ed. Brno: Masarykova univerzita, 2007, 120 pp. skripta. ISBN 978-80-210-4334-3. info
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 3., dopl. Praha: Academia, 1976, 669 s. URL 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 lecture complemented with an excercise to teach students needed computationals skills.
Assessment methods
Completion: Two written credit tests will be realized during the semester. It is required to obtain at least half of points in each test.
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 Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2019, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2019/MUC13