Course detail

# Mathematics 1

FEKT-BPA-MA1Acad. year: 2022/2023

Basic mathematical notions. Function, inverse function, sequences. Linear algebra and geometry. Vector spaces, basic notions,linear combination of vectors, linear dependence, independence vectors, base, dimension of a vector space. Matrices and determinants. Systems of linear equations and their solution. Differential calculus of one variable, limit, continuity, derivative of a function. Derivatives of higher orders, l´Hospital rule, behavior of a function. Integral calculus of fuctions of one variable, antiderivatives, indefinite integral. Methods of a direct integration. Integration by parts, substitution methods, integration of some elementary functions. Definite integral and its applications. Improper integral. Infinite number series, convergence criteria. Power series, Taylor theorem, Taylor series.

Language of instruction

Number of ECTS credits

Mode of study

Guarantor

Department

Offered to foreign students

Learning outcomes of the course unit

- decide whether vectors are linearly independent and whether they form a basis of a vector space;

- add and multiply matrices, compute the determinant of a square matrix to the 4x4 type, compute the rank and the inverse of a matrix;

- solve a system of linear equations;

- estimate the domains and sketch the grafs of elementary functions;

- compute limits and asymptots for the functions of one variable, use the L’Hospital rule to evaluate limits;

- differentiate and find the tangent to the graph of a function, find the Taylor ploynomial of a function near a given point;

- sketch the graph of a function including extrema, points of inflection and asymptotes;

- integrate using technics of integration, such as substitution, partial fractions and integration by parts;

- evaluate a definite integral including integration by parts and by a substitution for the definite integral;

- compute the area of a region using the definite integral, evaluate the inmproper integral;

- discuss the convergence of the number series, find the

set of the convergence for the power series.

Prerequisites

Co-requisites

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Course curriculum

2. Vectors and matrices.

3. Determinants, systems of linear equations.

4. Limits and the continuity of the functions of one variable.

5. The derivative of the functions of one variable.

6. The Taylor polynom and the l'Hospitalovo rule.

7. Graphing a function.

8. Antiderivatives, the per partes method and the substitution technic.

9. Integration of the rational functions.

10. Definite integral.

11. The aplications of the definite integral and the improper integral.

12. Series.

13. Power series and Taylor series.

Work placements

Aims

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

Recommended optional programme components

Prerequisites and corequisites

Basic literature

Recommended reading

Fong, Y., Wang, Y., Calculus, Springer, 2000. (EN)

eLearning

**eLearning:**currently opened course

#### Type of course unit

Lecture

Teacher / Lecturer

Syllabus

2. Vector - combination, dependence and independence of vectors, base and dimension of a vector space.

3. Matrices and determinants.

4. Systems of linear equations and their solution.

5. Differential calculus of one variable. Limit, continuity, derivative of a function.

6. Derivatives of higher order, Taylor theorem.

7. L'Hospital rule, behaviour of a function.

8. Integral calculus of functions of one variable, primitive function, indefinite integral. Methods of direct integration.

9. Per partes method and substitution method. Integration of some elementary functions.

10. Definite integral and its applications.

11. Improper integral.

12. Infinite number series, convergence criteria.

13. Power series, Taylor theorem, Taylor series.

Exercise in computer lab

Teacher / Lecturer

Syllabus

2. Matrices, determinants.

3. Solving a system of linear equations.

4. Derivative of a function of one variable.

5. Behaviour of a function.

6. Calculation of indefinite and definite integrals.

7. Series.

Project

Teacher / Lecturer

Syllabus

eLearning

**eLearning:**currently opened course