Czech

8

Not applicable.

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.

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

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

COURSE-UNIT CREDIT REQUIREMENTS: Active attendance at the seminars and at least one of the following written tests classified better than F(failed):

First test (Week 7):
Problem 1: Calculate a partial derivative.
Problem 2: Find maxima and minima of a function of several variables.
Problem 3: Determine the Taylor polynomial of a function.

Second test (Week 12):
Find the solution to three problems in double and triple integrals.

FORM OF EXAMINATIONS:
The exam has a written and an oral part.
In a 120-minute written test, students have to solve the following five problems:
Problem 1: Calculate a partial derivative, differential, directional derivative, gradient, sketch the domain of a function of two variables, determine the tangent plane and normal to the graph of a two function.
Problem 2: In differential calculus of functions of several variables.
Problem 3: Calculate a double or triple integral.
Problem 4: Calculate a line or surface integral, determine the potential to a function.
Problem 5: A theoretical question or a simple problem to test the knowledge acquired within the course.

During the oral part of the exam, the examiner will go through the test with the student.

The examiner should inform the students at the last lecture at the least about the basic rules of the exam and the assessment of its results.

RULES FOR CLASIFICATION:
Problem one: 2 points.
Problem two to four: five points each.
Problem five: 3 points.
Therefore, the student may achieve 20 points in total.

Final classification:
A (excellent): 20,19 points.
B (very good): 18,17 points.
C (good): 16,15 points.
D (satisfactory): 14,13 points.
E (sufficient): 12,11,10 points.
F (failed): 0 to 9 points.

Not applicable.

Not applicable.

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.

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.

Not applicable.

Not applicable.

Thomas G.B. - Finney R.L.: Calculus and Analytic Geometry, 7th edition
Sneall D.B. - Hosack J.M.: Calculus, An Integrated Approach
Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL Praha, 1988)
Thomas G. B.: Calculus (Addison Wesley, 2003)
Satunino, L.S., Hille, E., Etgen, J.G.: Calculus: One and Several Variables, Wiley 2002

Karásek J.: Matematika II (skriptum VUT)
Mezník I. - Karásek J. - Miklíček J.: Matematika I pro strojní fakulty (SNTL 1992)
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)
Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL, 1988)

8 hours, compulsory

Seminars in a computer lab have the programme MAPLE as a computer support. Obligatory topics to go through: Plotting of the graph of a function of more variables (given by explicit, implicit or parametric equations), extrema of functions of more variables.