Course detail
Mathematical Analysis I F
FSI-TA1 Acad. year: 2021/2022 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
7
Supervisor
Department
Learning outcomes of the course unit
Application of calculus methods in physical and technical disciplines.
Prerequisites
Secondary school mathematics knowledge.
Planned learning activities and teaching methods
The course is lectured through lessons supported by exercises at seminars. The content of lessons is focused on a theoretical background of the subject. The exercises have a practical/computational character.
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 the theory. A detailed information will be disclosed in advance before the exam.
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.
Specification of controlled education, way of implementation and compensation for absences
Seminars: obligatory.
Lectures: recommended.
The study programmes with the given course
Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, compulsory
Type of course unit
Lecture
52 hours, optionally
Teacher / Lecturer
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
Teacher / Lecturer
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.