Course unit code: 
FSI2MA 
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: 
8 
Learning outcomes of the course unit:
Students will be made familiar with differential and integral calculus of more variables. They will be able to apply this knowledge in various engineering tasks. After completing the course students will be prepared for further study of physics, mechanics and other technical disciplines.


Mode of delivery:
90 % facetoface, 10 % distance learning


Prerequisites:
Linear algebra, differential and integral calculus of functions of one variable.


Corequisites:
Not applicable.


Recommended optional programme components:
Not applicable.


Course contents (annotation):
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. Also dealt are the line and surface integrals both in a scalar and a vector field. At seminars, the MAPLE mathematical software is used.


Recommended or required reading:
Thomas G.B.  Finney R.L.: Calculus and Analytic Geometry, 7th edition Karásek J.: Matematika II (skriptum VUT) Mezník I.  Karásek J.  Miklíček J.: Matematika I pro strojní fakulty (SNTL 1992) Sneall D.B.  Hosack J.M.: Calculus, An Integrated Approach Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL Praha, 1988) Děmidovič B. P.: Sbírka úloh a cvičení z matematické analýzy Eliáš J., Horváth J., Kajan J.: Zbierka úloh z vyššej matematiky I, II, III, IV (Alfa Bratislava, 1985) Thomas G. B.: Calculus (Addison Wesley, 2003) Satunino, L.S., Hille, E., Etgen, J.G.: Calculus: One and Several Variables, Wiley 2002 Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL, 1988)


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 four problems:
Problem 1: In basic properties of functions of several variables: domains, partial derivatives, gradient (at most 10 points)
Problem 2: In differential calculus of functions of several variables (at most 20 points)
Problem 3: In double and tripple integral (at most 20 points)
Problem 4: In line and surface integral (at most 20 points)
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:
English


Work placements:
Not applicable.


Course curriculum:
Not applicable.


Aims:
The course aims to acquaint the students with the basics of differential and integral calculus of functions of several variables. This will enable them to attend engineering courses and deal with engineering problems. 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. The way of compensation for an absence is fully at the discretion of the teacher.

