Course detail

Mathematics 1

FEKT-AMA1Acad. year: 2012/2013

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.

Language of instruction

Czech

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

Student is able after complete the subject:
- to use the formal mathematical language to formulate simple statements especially about relations between learned objects
- to formulate and understand the key mathematical concepts, method of deductive thinking
- to explain characteristics and possibility of usage of function of one real variable by solving the basic practical tasks
- to solve these practical tasks (optimization, summation) with mathematical methods
- to use methods of linear algebra for modeling the practical tasks and solve them afterwards
- to use a modern mathematical softwafre for solving these tasks.

Prerequisites

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

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

Course curriculum

1. Sets, functions and the inverse function.
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

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Brabec B., Hrůza,B., Matematická analýza II, SNTL, Praha, 1986.
Edwards, C.H., Penney, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993.
Fong, Y., Wang, Y., Calculus, Springer, 2000
Ross, K.A., Elementary analysis: The Theory of Calculus, Springer, 2000.
Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997.
Thomas, G.B., Finney, R.L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BTBIO-A Bachelor's

    branch A-BTB , 1 year of study, winter semester, compulsory

  • Programme EEKR-CZV lifelong learning

    branch EE-FLE , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

RNDr. Vlasta Krupková, CSc.

Syllabus

1. Basic mathematical notions, function, sequence.
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

13 hod., compulsory

Teacher / Lecturer

RNDr. Vlasta Krupková, CSc.

Syllabus

1. Graphs of elementary functions, inverse functions, .
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.