Course detail

Mathematics 2

FP-Bma2PAcad. year: 2022/2023

The subject is part of the theoretical basis of the field. The goal is to teach students to understand the use of the apparatus of number series, Taylor's method for the approximate calculation of function values, the indefinite and definite integral of a function of 1 variable, the solution of 2 types of selected differential equations, the basics of the theory of functions of 2 real variables, the basics of logic and graph theory (including applications in economic disciplines).

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. RNDr. Bedřich Půža, CSc.

Department

Institute of Informatics (ÚI)

Learning outcomes of the course unit

Získané vědomosti a praktické matematické dovednosti budou zejména oporou pro získávání dalších vědomostí a rozšiřování dalších dovedností v oborech s ekonomickým zaměřením, pro korektní využívání matematických software a dále důležitým východiskem pro osvojování nových poznatků v předmětech matematického charakteru.

Prerequisites

Knowledge of secondary-school mathematics and successful completion of the course “Mathematics I”.

Co-requisites

Not applicable.

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

Credit requirements:

Passing control tests and achieving at least 55% points or passing a comprehensive written work and achieving at least 55% points.
Awarding credit is a necessary condition for taking the exam.

Exam requirements:

The exam has a written and an oral part, with the focus of the exam being the oral part.

For all tasks in the written part, the calculation must be written down, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.


Completion of the subject for students with individual study:
Passing the comprehensive control test and achieving at least 55% points.
Awarding credit is a necessary condition for taking the exam.
The exam has a written and an oral part, with the focus of the exam being the oral part.
For all tasks in the written part, the calculation must be written down, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.

Course curriculum

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.

Work placements

Not applicable.

Aims

Cílem je naučit studenty aplikovat uvedené poznatky a metody k analýze praktických procesů popsaných uvedenými matematickými modely a řešit je včetně aplikací v ekonomických disciplínách (výpočty realizovat i s ohledem na používání výpočetní techniky).

Specification of controlled education, way of implementation and compensation for absences

Attendance at exercises (seminars) is controlled.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

MEZNÍK, I. Diskrétní matematika pro užitou informatiku. CERM. CERM. Brno: CERM, s.r.o., 2013. 185 s. ISBN: 978-80-214-4761- 5. (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.: Matematika II. FP VUT v Brně, Brno 2009

Recommended reading

Not applicable.

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BAK-PM Bachelor's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

Mgr. Martina Bobalová, Ph.D.

Syllabus

1. Course of function I (monotonicity, local and absolute extrema of the function)
2. Course of the function II (convexity and concavity, asymptotes of the function, complete description of the behavior of the function)
3. Indefinite integral (meaning, properties, basic rules for calculation)
4. Integration methods I (per partes and substitution method)
5. Methods of integration II (decomposition into partial fractions, integration of rational fractional functions)
6. Definite integral (meaning, properties, calculation rules, applications, improper integral)
7. Summary (function progression, function integral)
8. Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)
9. Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
10. Bound extrema (Lagrange method)
11. Differential equations of the 1st order with separated variables
12. Summary (definite integral, differential equation, introduction to functions of several variables)
13. Linear differential equation of the 1st order

Exercise

26 hod., compulsory

Teacher / Lecturer

Mgr. Martina Bobalová, Ph.D.

Syllabus

  1. Differential and derivatives of higher orders (differential and its use, derivatives of higher orders, l'Hospital's rule)
  2. Course of function I (monotonicity, local and absolute extrema of the function, convexity and concavity, asymptotes of the function)
  3. Progress of the function II (full description of the behavior of the function)
  4. Indefinite integral (meaning, properties, basic rules for calculation)
  5. Integration methods I (per partes and substitution method)
  6. Methods of integration II (decomposition into partial fractions, integration of rational fractional functions)
  7. Definite integral (meaning, properties, rules for calculation)
  8. Application of a definite integral
  9. Functions of multiple variables and partial derivatives (graph and its sections, partial derivatives, differential)
  10. Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
  11. Bound extrema of functions of several variables
  12. Differential equation of the 1st order with separated variables
  13. Linear differential equation of the 1st order

Elearning

eLearning: currently opened course