Course detail

# Mathematical Analysis II

FSI-SA2CompulsoryBachelor's (1st cycle)Acad. year: 2016/2017Summer semester1. year of study8  credits

The course Mathematical Analysis II is directly linked to the introductory course Mathematical Analysis I. It concerns differential and integral calculus of functions in several real variables. Students will acquire theoretical background that is necessary in solving some particular problems in mathematics as well as in technical disciplines.

Learning outcomes of the course unit

Use of several variable calculus methods in physical and technical problems.

Mode of delivery

90 % face-to-face, 10 % distance learning

Prerequisites

Mathematical Analysis I, Linear Algebra.

Co-requisites

Not applicable.

Recommended optional programme components

Calculus with MAPLE.

V. Jarník: Diferenciální počet II, Academia, 1984. (CS)
J. Karásek: Matematika II, skripta FSI VUT, 2002. (CS)
V. Jarník: Integrální počet II, Academia, 1984. (CS)
D. M. Bressoud: Second Year Calculus, Springer, 2001. (EN)
J. Škrášek, Z. Tichý: Základy aplikované matematiky I a II, SNTL Praha, 1989. (CS)

Planned learning activities and teaching methods

The course is lectured through lessons supported by exercises. 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., receiving at least one half of all possible points from each of them).

Exam: will have both a written part as well as an oral part, a condition for admission to the oral part is receiving at one half of all possible points from the written part).

Language of instruction

Czech

Work placements

Not applicable.

Aims

Students should get familiar with basics of differential and integral calculus in several real variables. With such knowledge, various tasks of physical and engineering problems can be solved.

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

Seminars: obligatory.
Lectures: recommended.

#### Type of course unit

Lecture

52 hours, optionally

Teacher / Lecturer

Syllabus

1. Metric spaces;
2. Mappings between metric spaces, function of several variables;
3. Limit and continuity;
4. Partial derivatives, directional derivative, gradient;
5. Total differential, Taylor polynomial;
6. Local extremes;
7. Extremes subject to constraints and absolute extremes.
8. Functions defined implicitly;
9. Double and triple integral;
10. Applications of double and triple integrals, curves and their orientations;
11. Line integrals, Green's theorem;
12. Path independence for line integrals and related notions, surfaces and their orientability;
13. Surface integrals and its applications, Gauss–Ostrogradskii's theorem and Stokes' theorem.

seminars

33 hours, compulsory

Teacher / Lecturer

Syllabus

Seminars are related to the lectures in the previous week.

seminars in computer labs

6 hours, compulsory

Teacher / Lecturer

Syllabus

This seminar is supposed to be computer assisted.