Course detail
Mathematical Analysis I F
FSI-TA1 Acad. year: 2025/2026 Winter semester
Supervisor
Department
Learning outcomes of the course unit
Prerequisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course-unit credit: active attendance at the seminars, successful passing through two written tests (i.e. from each of them, it is necessary to reach at least one half of all the possible points).
Exam: will have an oral form with focus on theory. Detailed information will be disclosed in advance before the exam.
Seminars: obligatory.
Lectures: recommended.
Language of instruction
Czech
Aims
The goal is to acquire knowledge of the fundamentals of differential and integral calculus of one real variable functions. Beside 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.
Specification of controlled education, way of implementation and compensation for absences
The study programmes with the given course
Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's
branch ---: no specialisation, 7 credits, 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.