Course detail
Mathematical Analysis II
FSI-SA2 Acad. year: 2025/2026 Summer semester
Supervisor
Department
Learning outcomes of the course unit
Prerequisites
Planned learning activities and teaching methods
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 an oral form with focus on theory. Detailed information will be disclosed in advance before the exam.
Seminars: obligatory.
Lectures: recommended.
Language of instruction
Czech
Aims
Specification of controlled education, way of implementation and compensation for absences
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's
branch ---: no specialisation, 7 credits, compulsory
Type of course unit
Lecture
52 hours, optionally
Syllabus
1. Metric spaces, convergence in a metric space;
2. Complete and compact metric spaces, mappings between metric spaces;
3. Function of several variables, limit and continuity;
4. Partial derivatives, directional derivative, gradient;
5. Total differential, Taylor polynomial;
6. Local and global extrema;
7. Implicit functions, differentiable mappings between higher dimensional spaces;
8. Constrained extrema, double integral;
9. Double integral over measurable sets, triple integral;
10. Substitution in a double and triple integral, selected applications;
11. Plane and space curves, line integrals, Green's theorem;
12. Path independence for line integrals and related notions, space surfaces;
13. Surface integrals, Gauss-Ostrogradsky's theorem and Stokes' theorem.
Exercise
33 hours, compulsory
Syllabus
Seminars are related to the lectures in the previous week.
Computer-assisted exercise
6 hours, compulsory
Syllabus
This seminar is supposed to be computer assisted.