FP-MA2_MAcad. year: 2020/2021
This course follows Mathematics I course. Content is linear algebra, differential calculus of several variables, differential and difference equations (mainly linear) and instruments for their only solution - power series and Fourier series and selected integral transformation.
Learning outcomes of the course unit
Acquired knowledge and practical mathematical skills will be an important starting point for mastering new knowledge in the follow-up courses of mathematical character; they will also be essential for acquiring knowledge in courses on economy and for the correct use of mathematical software.
Knowledge of secondary-school mathematics and successful completion of the course “Mathematics I”.
Recommended optional programme components
Recommended or required reading
Mezník,I.: Matematika II.FP VUT v Brně, Brno 2009 (CS)
Mezník, I: Diskrétní matematika. FP VUT v Brně v Akademickém nakladatelství CERM, s.r.o. Brno, Brno 2004. ISBN 80-214-2754-X. (CS) (CS)
MEZNÍK, I. Základy matematiky pro ekonomii a management. Základy matematiky pro ekonomii a management. 2017. s. 5-443. ISBN: 978-80-214-5522-1. (CS)
Planned learning activities and teaching methods
Instructing is divided into lectures and exercises. Lectures are focused on the theory referring to applications, exercises on practical calculations and solving of application tasks.
Assesment methods and criteria linked to learning outcomes
Conditions for awarding course-unit credits:
-active participation in the seminars where the attendance is compulsory,
-fulfilment of individual tasks and successful completion of written assignments,
-working out of a semester project marked with at least “E”,
-completion of partial written exams marked more than 55% points
The exam has a written and an oral part with the written part being more important.
Language of instruction
1. Sequences (bounded and monotone sequences of real numbers, limits of sequences)
2. Derivation of the 1st order (meaning, basic properties and rules, derivation of elementary functions)
3. Derivation of 1st and higher orders (differential and its use, derivation of higher orders, l´Hospital's rule)
4. Course of function I (monotonicity, local and absolute extrema of function)
5. Course of function II (convexity and concavity; asymptotes of function, complete description of function behavior)
6. Indefinite integral (sense, properties, condition of existence, basic rules for calculation, integrals of some elementary functions)
7. Integration methods (per partes and substitution method, integration of simple rational functions)
8. Definite integral (sense, properties, rules for calculation, other applications, improper integral)
9. 1st order differential equations (with separated variables, linear)
10. Linear differential equations of the 2nd order (with constant coefficients)
11. Functions of several variables (graph and its sections, partial derivatives of the 1st order, differential)
12. Partial derivatives of higher orders (interchangeability, local extrema)
13. Absolute and bounded extrema (on compact sets, Lagrange's method)
The aim of the course is to build up mathematical tools necessary for the instruction of specialized courses.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures and exercises (seminars) is not controlled.