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Course detail

Mathematical Analysis II

Course unit code: FSI-SA2
Academic year: 2016/2017
Type of course unit: compulsory
Level of course unit: Bachelor's (1st cycle)
Year of study: 1
Semester: summer
Number of ECTS credits:
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.
Course contents (annotation):
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.
Recommended or required reading:
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.
Course curriculum:
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: doc. Ing. Luděk Nechvátal, Ph.D.
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: doc. Ing. Luděk Nechvátal, Ph.D.
Mgr. Viera Štoudková Růžičková, Ph.D.
Syllabus: Seminars are related to the lectures in the previous week.
seminars in computer labs: 6 hours, compulsory
Teacher / Lecturer: doc. Ing. Luděk Nechvátal, Ph.D.
Syllabus: This seminar is supposed to be computer assisted.

The study programmes with the given course