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

Number of ECTS credits

Mode of study

Guarantor

Department

Entry knowledge

Rules for evaluation and completion of the course

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

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

Prerequisites and corequisites

Basic literature

Krupková, V., Fuchs, P., Matematika 1B (CS)

Recommended reading

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

#### Type of course unit

Lecture

Teacher / Lecturer

Syllabus

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

Teacher / Lecturer

Syllabus

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

Teacher / Lecturer

Syllabus

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