Course detail
Mathematical Analysis I
FSI-SA1 Acad. year: 2018/2019 Winter semester
A subject area main content consists in the 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
Learning outcomes of the course unit
Use 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 possible points).
Exam: will have both a written part as well as an oral part, a condition for admission to the oral part is receiving at least one half of all possible points from the written part).
Aims
The goal is to acquire knowledge of fundamentals of differential and integral calculus of one real variable functions. Beside theoretical background, students should be able to apply the calculus tools 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 B3A-P: Applied Sciences in Engineering, Bachelor's
branch B-FIN: Physical Engineering and Nanotechnology, compulsory
Programme B3A-P: Applied Sciences in Engineering, Bachelor's
branch B-MAI: Mathematical Engineering, 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;
3. Mappings, real numbers;
4. Real sequences;
5. Function of a real variable, elementary functions;
6. Limit and continuity of a function;
7. Derivative and differential of a function, higher order derivatives and differentials;
8. l'Hospital rule, Taylor polynomial;
9. Curve sketching;
10. Indefinite integral, basic types of integrals;
11. Methods of computing indefinite integrals;
12. Riemann integral, Newton-Leibniz formula;
13. Improper integrals, applications of Riemann integrals.
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.