Course detail
Mathematical Analysis II
FSI-SA2 Acad. year: 2025/2026 Summer semester
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 a theoretical background that is necessary in solving some particular problems in mathematics as well as in technical disciplines.
Language of instruction
Czech
Number of ECTS credits
7
Supervisor
Department
Entry knowledge
Mathematical Analysis I, Linear Algebra.
Rules for evaluation and completion of the course
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 be oral based (possibly will have also a written part). Students are supposed to discuss three selected topics from the lessons.
Seminars: obligatory.
Lectures: recommended.
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.
Application of several variable calculus methods in physical and technical problems.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, 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.