Course detail

Mathematics 1

FEKT-CMA1Acad. year: 2009/2010

Basic mathematical notions, functions and sequences. Vector spaces, linear combination of vectors, linear dependence and independence of vectors vectors, basis and dimension of vector space. Matrices and determinants. Systems of linear equations and their solutions.
Limit, continuity and derivative of function of one variable, derivatives of higher orders, Taylor polynomial, behavior of function, l´Hospital rule. Antiderivatives, indefinite integral of fuction of one variable, integration by parts, substitution method, integration of some elementary functions. Definite integral and its applications. Improper integral. Number series, power series, Taylor series. Limit, continuity and derivatives of function of several variables, gradient, derivatives of higher orders, total differential, Taylor polynomial, local extrema of functions of several variables.

Language of instruction

English

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

RNDr. Vlasta Krupková, CSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The ability of orientation in the basic problems of higher mathematics.

Prerequisites

Knowledge on the secondary school level.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Requirements for the completion of the course are specified by the lecturer responsible for the course.

Course curriculum

1. Systems of linear equations.
2. Determinant, inverse matrix.
3. Function, limit, continuity.
4. Derivative -- physical and mathematical meaning of the concept. Rules for creating derivatives.
5. Graph of function -- intervals with f(x) increasing, local extremal points.
6. Graph of function II -- intervals with f(x) convex, asymptote of the graph.
7. Integration -- relation between definite and indefinite integral, basic integration methods.
8. Definite integration.
9. Application of definite integral. Improper integral.
10. Infinite number series, criteria of convergence.
11. Infinite power series, radius of convergence.
12. Taylor polynomial, Taylor series.

Work placements

Not applicable.

Aims

The main goal of the course is to explain the basic principles and methods of higher mathematics that are necessary for the study of electrical engineering.

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

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EEKR-BC Bachelor's

    branch BC-AMT , 1. year of study, winter semester, compulsory
    branch BC-EST , 1. year of study, winter semester, compulsory
    branch BC-MET , 1. year of study, winter semester, compulsory
    branch BC-SEE , 1. year of study, winter semester, compulsory
    branch BC-TLI , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

RNDr. Vlasta Krupková, CSc.

Syllabus

1. Basic mathematical notions, functions and sequences.
2. Vectors, combination, dependence and independence of vectors, basis and dimension of vector space.
3. Matrices and determinants, systems of linear equations and their solutions.
4. Differential calculus of one variable, limit, continuity, derivative.
5. Derivatives of higher orders, Taylor polynomial, l'Hospital rule, behaviour of function.
6. Integral calculus of one variable, antiderivative, indefinite integral.
7. Integration by parts, substitution method, integration of some elementary functions.
8. Definite integral and its applications.
9. Improper integral.
10. Number series, criterions of convergence.
11. Power series, Taylor series.
12. Differential calculus of more variables, limit, continuity, partial derivatives, gradient.
13. Derivatives of higher orders, total differential, Taylor polynomial, local extrema of functions of several variables.

Fundamentals seminar

12 hours, optionally

Teacher / Lecturer

RNDr. Vlasta Krupková, CSc.

Exercise in computer lab

14 hours, optionally

Teacher / Lecturer

RNDr. Vlasta Krupková, CSc.