Course detail

Mathematics 2

FP-MA2_MAcad. year: 2022/2023

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.

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

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.

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

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.

Course curriculum

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 equation of the 1st order (with separated variables, linear)
9. Linear differential equation of the 2nd order (with constant coefficients)
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)

Work placements

Not applicable.

Aims

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 exercises (seminars) is controlled.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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)

Recommended reading

Not applicable.

eLearning

eLearning: currently opened course

Classification of course in study plans

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

  • Programme BAK-MIn-D Bachelor's

    branch BAK-MIn , 1. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Bedřich Půža, CSc.

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 equation of the 1st order with separated variables
  12. Summary (definite integral, function of several variables)
  13. Linear differential equation of the 1st order

Exercise

26 hours, compulsory

Teacher / Lecturer

Ing. Lukáš Podešva
doc. RNDr. Bedřich Půža, CSc.

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