Mathematical Analysis II (FSI-SA2)

Academic year 2025/2026
Supervisor: doc. Ing. Luděk Nechvátal, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:
 
Teaching methods and criteria:
 
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.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 4 hrs. optionally                  
    Exercise  11 × 3 hrs. compulsory                  
    Computer-assisted exercise  2 × 3 hrs. compulsory                  
Course curriculum:
    Lecture 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 Seminars are related to the lectures in the previous week.
    Computer-assisted exercise This seminar is supposed to be computer assisted.
Literature - fundamental:
1. V. Jarník: Diferenciální počet II, Academia, 1984.
2. V. Jarník: Integrální počet II, Academia, 1984.
3. D. M. Bressoud: Second Year Calculus, Springer, 2001.
4. J. Škrášek, Z. Tichý: Základy aplikované matematiky I a II, SNTL Praha, 1989.
5. J. Stewart: Multivariable Calculus (8th ed.), Cengage Learning, 2015.
6. C. Bray: Multivariable Calculus, CreateSpace Independent Publishing Platform, 2013.
7. P. D. Lax, M. S. Terrel: Multivariable Calculus with Applications, Springer, 2017.
Literature - recommended:
1. J. Karásek: Matematika II, skripta FSI VUT, 2002.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-MAI-P full-time study --- no specialisation -- Cr,Ex 7 Compulsory 1 1 S