Course detail

# Mathematics 1

Basic mathematical notions. Sets, operations with sets, concept of a 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.

Learning outcomes of the course unit

The ability of orientation in the basic problems of higher mathematics and the ability to apply the basic methods. Solving problems in the areas cited in the annotation above by using basic rules. Solving these problems by using modern mathematical software.

Prerequisites

Knowledge at secondary school level and of completed subjects in the study area

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

EDWARDS, C.H., PENNEY, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993. (EN)
BRABEC B., HRŮZA,B., Matematická analýza II, SNTL, Praha, 1986. (CS)
ROSS, K.A., Elementary analysis: The Theory of Calculus, Springer, 2000. (EN)
FONG, Y., WANG, Y., Calculus, Springer, 2000 (EN)
ŠVARC, S. a kol., Matematická analýza I, PC DIR, Brno, 1997. (CS)
THOMAS, G.B., FINNEY, R.L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994. (EN)

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 completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every

Language of instruction

Czech

Work placements

Not applicable.

Aims

The main goal of the calculus course is to explain the basic principles and methods of higher mathematics that are necessary for the study of electrical engineering. The practical aspects of application of these methods and their use in solving concrete problems (including the application of contemporary mathematical software) are emphasized.

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

Classification of course in study plans

• Programme BPC-STC Bachelor's, 1. year of study, winter semester, 7 credits, compulsory

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Computer-assisted exercise

39 hours, compulsory

Teacher / Lecturer

eLearning