Course detail
Mathematical Analysis I
FSI-SA1 Acad. year: 2025/2026 Winter semester
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
Supervisor
Department
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.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, compulsory
Type of course unit
Lecture
52 hours, optionally
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 hours, compulsory
Syllabus
Seminars are related to the lectures in the previous week.
Computer-assisted exercise
8 hours, compulsory
Syllabus
This seminar is supposed to be computer assisted.