Course detail

Mathematical Analysis II

FSI-SA2 Acad. year: 2025/2026 Summer semester

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.