Course detail

Mathematical Analysis II

FSI-SA2Acad. year: 2011/2012

The course “Mathematical Analysis II” is a follow-up to the introductory course “Mathematical Analysis I”. It deals with the differential and integral calculus of functions in one several variables. Students acquire theoretical knowledge in several variables functions necessary for solving of difficult problems in mathematics, physics and technical disciplines.

Language of instruction

Czech

Number of ECTS credits

8

Mode of study

Not applicable.

Guarantor

doc. RNDr. Miroslav Kureš, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Calculus count methods for applications in technical disciplines.

Prerequisites

The differential and integral calculus of functions in one real variable.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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 n real variables. 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

V. Jarník: Diferenciální počet II, Academia, 1984. (CS)
V. Jarník: Integrální počet II, Academia, 1984. (CS)
D. M. Bressoud: Second Year Calculus, Springer, 2001. (EN)

Recommended reading

J. Karásek: Matematika II, skripta FSI VUT, 2002. (CS)

Classification of course in study plans

  • Programme B3A-P Bachelor's

    branch B-MAI , 1. year of study, summer semester, compulsory

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

doc. RNDr. Miroslav Kureš, Ph.D.

Syllabus

1. Functions in several variables. Basic concepts.
2. Partial derivations. The gradient.
3. Total differentials. Taylor polynomials.
4. Local extremes.
5. Relative and absolute extremes.
6. Functions defined implicitly.
7. Double and triple integral.
8. Applications of double and triple integrals.
9. Curves and their orientations.
10. Line integrals and its applications. Green's theorem.
11. The potential, the nabla and delta operators, divergence and curl of a vector field.
12. Surfaces and their orientability.
13. Surface integrals and its applications. Gauss-Ostrogradskii's theorem and Stokes' theorem.

Exercise

39 hours, compulsory

Teacher / Lecturer

Mgr. Jana Hoderová, Ph.D.

Syllabus

Seminars related to the lectures in the previous week.