Course detail

Mathematics 1

FEKT-CMA1Acad. year: 2011/2012

Basic mathematical notions, functions and sequences. Vector spaces, linear combination of vectors, linear dependence and independence of 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.

Language of instruction

English

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

RNDr. Petr Fuchs, Ph.D.

Department

Department of Mathematics (UMAT)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

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

Prerequisites

The subject knowledge on the secondary school level is required.

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. 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 course is to explain the basic principles and methods of higher mathematics necessary for further studies.

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

The content and forms of the evaluated course are specified by the lecturer responsible for the course.

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

doc. RNDr. Zdeněk Šmarda, 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.
4. Systems of linear equations and their solutions.
5. Differential calculus of one variable, limit, continuity, derivative.
6. Derivatives of higher orders, Taylor polynomial.
7. L'Hospital rule, behaviour of function.
8. Integral calculus of one variable, antiderivative, indefinite integral.
9. Integration by parts, substitution method, integration of some elementary functions.
10. Definite integral and its applications.
11. Improper integral
12. Number series, criterions of convergence.
13. Power series, Taylor series.

Fundamentals seminar

12 hours, optionally

Teacher / Lecturer

doc. RNDr. Zdeněk Šmarda, CSc.

Exercise in computer lab

14 hours, optionally

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.