Course detail

Mathematics 2

FP-mat2PAcad. year: 2026/2027

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  indefinite and certain integrals of function 1, solutions of 2 types of selected differential equations, basics of the theory of functions of 2 real variables.

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

see the literature

Prerequisites and corequisites

Not applicable.

Basic literature

KLŮFA, Jindřich a SÝKOROVÁ, Irena, 2023. Učebnice matematiky (2) pro studenty VŠE. Jesenice: Ekopress. ISBN 978-80-87865-86-6. (CS)
MEZNÍK, Ivan, 2017. Základy matematiky pro ekonomii a management. Vyd. 2., rozš. Brno: Fakulta podnikatelská Vysokého učení technického v Brně v Akademickém nakladatelství CERM, s.r.o. Brno. ISBN 978-80-214-5522-1 (CS)

Recommended reading

JACQUES, Ian, 2023. Mathematics for economics and business. Harlow, England: Pearson, 2023. ISBN 978-1-292-19166-9. (EN)
HOFFMANN, Laurence D. a BRADLEY, Gerald L., 2007. Calculus for business, economics, and the social and life sciences. 10th ed. Boston: McGraw-Hill. ISBN 978-0-07-122024-8 (EN)

Classification of course in study plans

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

Type of course unit

 

Lecture

26 hours, compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

  1. Review of the material: calculus of functions of one variable.
  2. Indefinite integral (meaning, properties, basic rules for calculation).
  3. Integration methods I (per partes and substitution method).
  4. Methods of integration II (decomposition into partial fractions, integration of rational fractional functions).
  5. Definite integral (meaning, properties, calculation rules, applications, improper integral).
  6.  Applications of integral.
  7. Summary: integral and its applications.
  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. Constrained extrema (Lagrange method).
  11. Separable ordinary differential equations.
  12. First order linear differential equations. Second order linear differential equations with constant coefficients.
  13. Summary: functions of two variables, differential equations.

Exercise

26 hours, 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. Definite integral (application)
  9. Functions of multiple variables and partial derivatives (graph, partial derivatives, differential)
  10. Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
  11. Extrema of functions of several variables
    Differential equation of the 1st order with separated variables.
  12. Linear differential equations of the 1st order.

    Learning Outcomes:

    Professional Knowledge
    The student understands the theory of differential and integral calculus of functions of a single variable, as well as differential calculus of functions of several variables, including their practical applications.

    Professional Competence
    The student is able to choose and apply appropriate mathematical methods to solve models of real-world processes and to interpret the results in the context of their application.

    Professional Skills
    The student is capable of performing calculations involving integrals and extrema of functions of several variables, uses computational tools effectively, and interprets the results in practical contexts.

Self-study

60 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Individual preparation for an ending of the course

44 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.