FP-ma2PAcad. year: 2018/2019
The subject is part of the theoretical basis of the field. Learning outcomes of the course unit The aim of the course is to teach students how to use the numerical series apparatus, Taylor's method for approximate calculation of function values, indefinite and certain integrals of function 1, solutions of 2 types of selected differential equations, theory of functions of 2 real variables, logic bases and graph theory economic disciplines).
Learning outcomes of the course unit
The acquired knowledge and practical mathematical skills will be the mainstay for gaining further knowledge and spreading additional skills in economically oriented fields, for the correct use of mathematical software and an important starting point for acquiring new knowledge in subjects of mathematical character.
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. Základy matematiky pro ekonomii a management. Základy matematiky pro ekonomii a management. 2017. s. 5-443. ISBN: 978-80-214-5522-1. (CS)
MEZNÍK, I. Diskrétní matematika pro užitou informatiku. CERM. CERM. Brno: CERM, s.r.o., 2013. 185 s. ISBN: 978-80-214-4761- 5. (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,
-completion of one control test in the course of semester marked at least with “E”.
The exam has a written and an oral part with the written part being more important.
Language of instruction
The aim is to build up the mathematical apparatus necessary for the interpretation of follow-up professional subjects and to master the considerations and calculations in the field of the given subject matter (including with regard to the use of computer technology) including applications in computer science and economic disciplines. The acquired mathematical knowledge and practical computational skills are especially an important starting point for acquiring new knowledge in computer science and economically oriented fields, supporting the correct use of mathematical software, and for further expanding knowledge and skills in math mathematical subjects.
1. Sequences (limited and monotone sequences of real numbers, sequence limit).
2. First order derivations (sense, basic properties and rules, derivation of elementary functions).
3. Derivatives of the first and higher order (differential and its use, higher order derivation, l'Hospitality rule).
4. The course of function I (monotony, local and absolute extremes of function).
5. Function II (convexity and concavity, function asymptotes, full description of function behavior).
6. Indefinite integral (meaning, properties, condition of existence, basic rules for calculation, integrals of some elementary functions).
7. Integration methods (per partes and substitution methods, integration of simple rational functions).
8. Certain integral (meaning, properties, calculation rules, other applications, non-integral integral).
9. Differential equations of the first order (with separated variables, linear).
10. Linear differential equations of the 2nd order (with constant coefficients).
11. Function of multiple variables (graph and its cuts, 1st order partial derivation, differential).
12. Partial derivatives of higher order (interchangeability, local extrema).
13. Absolute and bound extremes (on compact sets, Lagrange method).
The aim is to teach students to apply the above mentioned knowledge and methods to analyze the practical processes described by these mathematical models and to solve them, including applications in economic disciplines (calculations to be performed with regard to the use of computer technology).
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is not controlled. Attendance at exercises (seminars) is compulsory and is regularly checked. A student is obliged to give reasons for his/her absence. If the teacher accepts the reason for the absence (which is completely under his/her competence), he/she will decide about the form of the compensation for the missed lessons.