Course unit code: 
FSIBMK 
Academic year: 
2016/2017 
Type of course unit: 
compulsory 
Level of course unit: 
Bachelor's (1st cycle) 
Year of study: 
1 
Semester: 
summer 
Number of ECTS credits: 
6 
Learning outcomes of the course unit:
Students will acquire basic knowledge of mathematical disciplines listed in the course annotation and will be made familiar with their logical structure. They will learn how to solve mathematical problems encountered when dealing with engineering tasks using the knowledge and skills acquired.


Mode of delivery:
20 % facetoface, 80 % distance learning


Prerequisites:
Differential and integral calculus of functions in one variable.


Corequisites:
Not applicable.


Recommended optional programme components:
Not applicable.


Course contents (annotation):
The course takes the form of lectures and seminars dealing with the following topics:
Real functions of two and more variables, Partial derivatives  total differentials, Applications of partial derivatives  maxima, minima and saddle points, Lagrange multipliers, Taylor's approximation and error estimates, Double integrals, Triple integrals, Applications of multiple integrals.


Recommended or required reading:
Rektorys, K. a spol.: Přehled užité matematiky I,II, , 0 Sneall, D. B., Hosack, J. M.: Calculus, An Integrated Approach, , 0 EIiáš, J., Horváth, J., Kajan, J.: Zbierka úloh z vyššej matematiky , , 0 Fichtengolc, G. M.: Kurz differencialnogo isčislenija, , 0


Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.


Assesment methods and criteria linked to learning outcomes:
COURSEUNIT CREDIT REQUIREMENTS: There are two written tests (each at most 12 points) within the seminars and a semestral work from the computer support (at most 1 point).
The student can obtain at most 25 points alltogether within the seminars. Condition for the courseunit credit: to obtain at least 6 points from each written test. Students, who do not fulfil conditions for the courseunit credit, can repeat the written test during first two weeks of examination time.
FORM OF EXAMINATIONS:
The exam has an obligatory written part.
In a 120minute written test, students have to solve the following three problems:
Problem 1: In differential calculus of functions of several variables.
Problem 2: In double integral.
Problem 3: In tripple integral.
Above problems can also contain a theoretical question.
RULES FOR CLASSIFICATION
1. Results from seminars (at most 25 points)
2. Results from the written examination (at most 75 points)
Final classification:
049 points: F
5059 points: E
6069 points: D
7079 points: C
8089 points: B
90100 points: A


Language of instruction:
Czech


Work placements:
Not applicable.


Course curriculum:
Not applicable.


Aims:
Differential and integral calculus of functions of several variables including problems of finding maxima and minima and calculating limits, derivatives, differentials, double and triple integrals. At seminars, the MAPLE mathematical software is used.
The course aims to acquaint the students with the theoretical basics of the above mentioned mathematical disciplines necessary for further study of engineering courses and for solving engineering problems encountered. Another goal of the course is to develop the students' logical thinking.


Specification of controlled education, way of implementation and compensation for absences:
Attendance at lectures is recommended, attendance at seminars is required. The lessons are planned on the basis of a weekly schedule. Missed seminars may be made up by the agreement with the teacher supervising the seminar.

