Course detail

Mathematics 1

FEKT-BPC-MA1BAcad. year: 2023/2024

Basic mathematical notions. Function, inverse function, sequences. 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. Multiple integral, transformation of a multiple integral, applications.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. RNDr. Edita Kolářová, Ph.D.

Department

Department of Mathematics (UMAT)

Entry knowledge

Students should be able to work with expressions and elementary functions within the scope of standard secondary school requirements; in particular, they shoud be able to transform and simplify expressions, solve basic equations and inequalities, and find the domain and the range of a function.

Rules for evaluation and completion of the course

The semester examination is rated at a maximum of 70 points.  It is possible to get a maximum of 30 points in practices for 3 written tests, each for maximun 10 points.
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.

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.
After completing the course, students should be able to:

- 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;
- 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.
- compute double and triple integral without a transformation;
- using transformation compute double and triple integral without a transformation;

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Kolářová, E: Matematika 1B - Sbírka úloh. (CS)
Krupková, V., Fuchs, P., Matematika 1B (CS)

Recommended reading

Brabec, B., Hrůza, B., Matematická analýza II, SNTL, Praha, 1986. (CS)
Edwards, C.H., Penney, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993. (EN)
Fong, Y., Wang, Y., Calculus, Springer, 2000. (EN)
Kolářová, E: Maple. (CS)
Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997. (CS)

eLearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BPC-AMT Bachelor's, 1. year of study, winter semester, compulsory
  • Programme BPC-SEE Bachelor's, 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

doc. RNDr. Edita Kolářová, Ph.D.

Syllabus

1. Sets, functions and the inverse function.
2. Limits and the continuity of the functions of one variable.
3. The derivative of the functions of one variable.
4. Local and absolute extrema of a function.
5. L'Hospital rule, graphing a function.
6. Antiderivatives, the per partes method and the substitution technique.
7. Integration of the rational and irrational functions.
8. Definite integral.
9. Aplications of the definite integral and the improper integral.
10. Number and power series.
11. Multiple integral.
12. Transformation of multiple integrals.
13. Applications of multiple integrals.

Fundamentals seminar

8 hours, compulsory

Teacher / Lecturer

doc. RNDr. Edita Kolářová, Ph.D.
Ing. Aleš Krček
Dr. RNDr. Karel Lepka, Ph.D.

Syllabus

1. Sets, functions and the inverse function.
2. Limits and the continuity of the functions of one variable.
3. The derivative of the functions of one variable.
6. Antiderivatives, the per partes method and the substitution technique.

Computer-assisted exercise

18 hours, compulsory

Teacher / Lecturer

doc. RNDr. Edita Kolářová, Ph.D.
Ing. Aleš Krček
Dr. RNDr. Karel Lepka, Ph.D.

Syllabus

4. Local and absolute extrema of a function.
5. L'Hospital rule, graphing a function.
7. Integration of the rational and irrational functions.
8. Definite integral.
9. Aplications of the definite integral and the improper integral.
10. Number and power series.
11. Multiple integral.
12. Transformation of multiple integrals.
13. Applications of multiple integrals.

eLearning

eLearning: currently opened course