Course detail

Mathematical Analysis I

FSI-SA1Acad. year: 2015/2016

In the introductory course “Mathematical Analysis I”, students majoring in Mathematical Engineering are familiarised with the fundamental concepts of differential and integral calculus of functions in one real variable. The acquired knowledge is a starting point not only for further study of Mathematical Analysis, but also a necessary assumption for study of physics and theoretical technical disciplines, as well as for practical solving of problems in these disciplines.

Language of instruction

Czech

Number of ECTS credits

8

Mode of study

Not applicable.

Guarantor

doc. Ing. Luděk Nechvátal, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Calculus count methods for applications in technical disciplines.

Prerequisites

Knowledge of mathematics in secondary school level.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course-unit credit is conditional on attendance. Examination: oral

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Students will be made familiar with fundaments of differential and integral calculus in one real variable. They will be able to apply it in various engineering tasks.

Specification of controlled education, way of implementation and compensation for absences

Seminars: required
Lectures: recommended

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

G. Strang: Calculus, 2nd ed., Wellesley–Cambridge Press, 2010. (EN)
J. Škrášek, Z. Tichý: Základy aplikované matematiky I a II, SNTL Praha, 1989. (CS)
V. Jarník: Diferenciální počet I, Academia, 1984. (CS)
V. Jarník: Integrální počet I, Academia, 1984. (CS)

Recommended reading

V. Novák: Diferenciální počet v R, 2. vyd., Masarykova univerzita, 1997. (CS)
V. Novák: Integrální počet v R, 3. vyd., Masarykova univerzita, 2001. (CS)

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B-MAI , 1 year of study, winter semester, compulsory
    branch B-FIN , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

52 hod., optionally

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.

Syllabus

1. Functions. Basic concepts.
2. Polynomials. Roots of polynomials.
3. Sequences. Limits.
4. Limits of functions. The continuity.
5. Derivations. The L'Hospital rule.
6. Differentials. Higher order derivations and differentials. Taylor polynomials.
7. Stationary points and extremes.
8. Inflection points. Asymptotes.
9. Curves.
10. The indefinite integral.
11. Methods of integration.
12. The Riemann integral.
13. Applications of the Riemann integral.

Exercise

33 hod., compulsory

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.
doc. Mgr. Zdeněk Opluštil, Ph.D.

Syllabus

Seminars related to the lectures in the previous week.

Computer-assisted exercise

6 hod., compulsory

Teacher / Lecturer

doc. Ing. Luděk Nechvátal, Ph.D.

Syllabus

Seminars in a computer lab have the programme MAPLE as a computer support. Obligatory topics to go through: Elementary arithmetic, calculations and evaluation of expressions, solving equations, finding roots of polynomials, graph of a function of one real variable, symbolic computations.