Course detail

Mathematics 2

FP-ma2PAcad. year: 2024/2025

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).

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

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

Rules for evaluation and completion of the course

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.


Attendance at exercises (seminars) is controlled.

Aims

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).
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.

Study aids

Viz. literature

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 (CS)

Recommended reading

Not applicable.

Classification of course in study plans

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

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, 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. Differential equations of the 1st order with separated variables
9. Linear differential equation of the 1st order
10. Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)
11. Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
12. Summary (definite integral, differential equation, introduction to functions of several variables)
13. Bound extrema (Lagrange method)

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, 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)
3. Course of the function II (convexity and concavity, asymptotes of the function, complete 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. Differential equations of the 1st order with separated variables
10. Linear differential equation of the 1st order
11. Linear differential equation of the 1st order
12. Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)
13. Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)