Mathematical Analysis I (FSI-SA1)

Academic year 2023/2024
Supervisor: doc. Ing. Luděk Nechvátal, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:

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.
Learning outcomes and competences:
Application of calculus methods in physical and technical disciplines.
Prerequisites:
Secondary school mathematics knowledge.
Course contents:
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.
Teaching methods and criteria:
The course is lectured via lessons supported by exercises at the seminars. The content of lessons is focused on the 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 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.
Controlled participation in lessons:
Seminars: obligatory.
Lectures: recommended.
Type of course unit:
    Lecture  13 × 4 hrs. optionally                  
    Exercise  11 × 4 hrs. compulsory                  
    Computer-assisted exercise  2 × 4 hrs. compulsory                  
Course curriculum:
    Lecture 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 Seminars are related to the lectures in the previous week.
    Computer-assisted exercise This seminar is supposed to be computer assisted.
Literature - fundamental:
1. V. Jarník: Diferenciální počet I, Academia, 1984.
2. V. Jarník: Integrální počet I, Academia, 1984.
3. G. Strang: Calculus, 2nd ed., Wellesley–Cambridge Press, 2010.
4. J. Škrášek, Z. Tichý: Základy aplikované matematiky I a II, SNTL Praha, 1989.
5. J. Stewart: Single Variable Calculus, 8th Edition, Cengage Learning, 2015.
6. M. Kline: Calculus: An Intuitive and Physical Approach, 2nd Edition, Dover Publications, 2013.
Literature - recommended:
1. V. Novák: Diferenciální počet v R, 2. vyd., Masarykova univerzita, 1997.
2. V. Novák: Integrální počet v R, 3. vyd., Masarykova univerzita, 2001.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-MAI-P full-time study --- no specialisation -- Cr,Ex 8 Compulsory 1 1 W