Course detail

Mathematical Analysis I

FSI-SA1Acad. year: 2025/2026

The subject area main content consists of differential and integral calculus of a one variable function. The acquired knowledge is a starting point for further study of mathematical analysis and related mathematical disciplines, and it serves as a theoretical background for study of physical and technical disciplines as well.

Language of instruction

Czech

Number of ECTS credits

8

Mode of study

Not applicable.

Guarantor

doc. Ing. Luděk Nechvátal, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Secondary school mathematics knowledge.

Rules for evaluation and completion of the course

Course-unit credit: active attendance at the seminars, successful passing through two written tests (i.e., from each of them, it is necessary to attain at least one half of all the possible points).

Exam: will have an oral form with focus on theory. A detailed information will be disclosed in advance before the exam.


Seminars: obligatory.
Lectures: recommended.

Aims

The objective is to acquire knowledge of the fundamentals of differential and integral calculus of one real variable functions. Besides the theoretical background, the students should be able to apply calculus tools in various technical problems.


Application of calculus methods in physical and technical disciplines.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

G. Strang: Calculus, 2nd ed., Wellesley–Cambridge Press, 2010. (EN)
J. Stewart: Single Variable Calculus, 8th Edition, Cengage Learning, 2015. (EN)
J. Škrášek, Z. Tichý: Základy aplikované matematiky I a II, SNTL Praha, 1989. (CS)
M. Kline: Calculus: An Intuitive and Physical Approach, 2nd Edition, Dover Publications, 2013. (EN)
V. Jarník: Diferenciální počet I, Academia, 1984. (CS)
V. Jarník: Integrální počet I, Academia, 1984. (CS)

Recommended reading

V. Novák: Diferenciální počet v R, 2. vyd., Masarykova univerzita, 1997. (CS)
V. Novák: Integrální počet v R, 3. vyd., Masarykova univerzita, 2001. (CS)

Classification of course in study plans

  • Programme B-MAI-P Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

52 hod., optionally

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.

Syllabus

1. Introduction to mathematical logic, logical essentials of mathematics;
2. Sets, relations between sets (and on a set);
3. Mappings, real numbers;
4. Real sequences;
5. Function of a real variable, basic elementary functions;
6. Polynomials and rational functions;
7. Limit and continuity of a function;
8. Derivative and differential of a function, higher order derivatives and differentials;
9. Theorems about differentiation, Taylor polynomial;
10. Curve sketching;
11. Primitive function and indefinite integral, integration techniques;
12. Riemann definite integral, Newton-Leibniz formula, properties;
13. Definite integral with a variable upper limit, improper integrals, applications.

Exercise

44 hod., compulsory

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.

Syllabus

Seminars are related to the lectures in the previous week.

Computer-assisted exercise

8 hod., compulsory

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.

Syllabus

This seminar is supposed to be computer assisted.