Mathematical Analysis I (FSI-SA1-A)

Academic year 2018/2019
Supervisor: doc. Ing. Luděk Nechvátal, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: English
Aims of the course unit:
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.
Learning outcomes and competences:
Use of calculus methods in physical and technical disciplines.
Prerequisites:
Secondary school mathematics knowledge.
Course contents:
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.
Teaching methods and criteria:
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).
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;
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 Seminars are related to the lectures in the previous week.
    Computer-assisted exercise This seminar is supposed to be computer assisted.
Literature - fundamental:
1. S. L. Salas, E. Hille, G. J. Etgen: Calculus: One and Several Variables, 10th ed., Wiley, 2006.
2. G. Strang: Calculus, 2nd ed., Wellesley–Cambridge Press, 2010
3. M. Spivak: Calculus, 4th ed., Publish or Perish, 2008
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3A-A full-time study B-MAI Mathematical Engineering -- Cr,Ex 8 Compulsory 1 1 W