Course detail

Mathematical Analysis II

FSI-SA2Acad. year: 2019/2020

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 the theoretical background that is necessary in solving some particular problems in mathematics as well as in technical disciplines.

Learning outcomes of the course unit

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


Mathematical Analysis I, Linear Algebra.


Not applicable.

Recommended optional programme components

Not applicable.

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, the condition for admission to the oral part is receiving at least one half of all possible points from the written part).

Language of instruction


Work placements

Not applicable.


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.

Classification of course in study plans

  • Programme B-MAI-P Bachelor's, 1. year of study, summer semester, 8 credits, compulsory

Type of course unit



52 hours, optionally

Teacher / Lecturer


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, smooth mappings from R^n to R^m;
8. Extrema subject to constraints, double integral;
9. Triple integral, alternative approach to multiple integrals;
10. Substitution in a double and a triple integral, applications;
11. Plane and space curves, line integrals, Green's theorem;
12. Path independence for the line integrals and related notions, space surfaces;
13. Surface integrals, Gauss-Ostrogradsky's theorem and Stokes' theorem.


33 hours, compulsory

Teacher / Lecturer


Seminars are related to the lectures in the previous week.

Computer-assisted exercise

6 hours, compulsory

Teacher / Lecturer


This seminar is supposed to be computer assisted.


eLearning: opened course