doc. RNDr. Zdeněk Šmarda, CSc.

Department of Mathematics (UMAT)

Students completing this course should be able to:
- calculate local, constrained and absolute extrema of functions of several variables.
- calculate multiple integrals on elementary regions.
- transform integrals into polar, cylindrical and sferical coordinates.
- calculate line and surface integrals in scalar-valued and vector-valued fields.
- apply integral theorems in the field theory.

The student should be able to apply the basic knowledge of analytic geometry and mathamatical analysis on the secondary school level: to explain the notions of general, parametric equations of lines and surfaces and elementary functions. From the BMA1 and BMA2 courses, the basic knowledge of differential and integral calculus and solution methods of linear differential equations with constant coefficients is demanded. Especially, the student should be able to calculate derivative (including partial derivatives) and integral of elementary functions.

Not applicable.

Not applicable.

ŠMARDA, Z., RUŽIČKOVÁ, I.: Vybrané partie z matematiky, el. texty na PC síti. (CS)
KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123s. (CS)
BRABEC, J., HRUZA, B.: Matematická analýza II, SNTL/ALFA, Praha 1986, 579s. (CS)
GARNER, L.E.: Calculus and Analytical Geometry. Brigham Young University, Dellen publishing Company, San Francisco,1988, ISBN 0-02-340590-2. (EN)

Teaching methods include lectures and demonstration practical classes (computer and numerical) . Course is taking advantage of exercise bank and maplets on UMAT server.

The student's work during the semestr (written tests and homework) is assessed by maximum 30 points.
Written examination is evaluated by maximum 70 points. It consist of seven tasks (one from extrema of functions of several variables (10 points), two from multiple integrals (2 X 10 points), two from line integrals (2 x 10 points) and two from surface integrals (2 x 10 points)).

Czech

Not applicable.

1) Differential calculus of functions of several variables, limit, continuity, derivative
2) Vector analysis
3) Local extrema
4) Constrained and absolute extrema
5) Multiple integral
6) Transformation of multiple integrals
7) Applications of multiple integrals
8) Line integral in a scalar-valued field.
9) Line integral in a vector-valued field.
10) Potential, Green's theorem
11) Surface integral in a scalar-valued field.
12) Surface integral in a vector-valued field.
13) Integral theorems.

The aim of this course is to introduce the basics of theory and calculation methods of local and absolute extrema of functions of several variables, double and triple integrals, line and surface integrals including applications in technical fields.
Mastering basic calculations of multiple integrals, especialy tranformations of multiple integrals and calculations of line and surface integrals in scalar-valued and vector-valued fields.
of a stability of solutions of differential equations and applications of selected functions
with solving of dynamical systems.

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

• Programme BPC-AUD Bachelor's

  specialization AUDB-ZVUK , any year of study, winter semester, 5 credits, optional
  specialization AUDB-TECH , any year of study, winter semester, 5 credits, optional
  

• Programme BPC-AMT Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BPC-EKT Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BKC-EKT Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BPC-IBE Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BPC-MET Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BKC-MET Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BKC-SEE Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BPC-SEE Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BKC-TLI Bachelor's, any year of study, winter semester, 5 credits, optional
  
• Programme BPC-TLI Bachelor's, any year of study, winter semester, 5 credits, optional
  

14 hours, compulsory

doc. RNDr. Zdeněk Šmarda, CSc.

eLearning: currently opened course