Course detail

# Mathematics II

FSI-2MAcad. year: 2022/2023

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.

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Assesment methods and criteria linked to learning outcomes

FORM OF EXAMINATIONS:

The exam has a written part (at most 75 points) and an oral part (at most 25 points).

WRITTEN PART OF EXAMINATION (at most 75 points)

In a 120-minute 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 22 points)

Problem 3: In double and triple integral (at most 20 points)

Problem 4: In line and surface integral (at most 23 points)

The above problems can also contain a theoretical question.

ORAL PART OF EXAMINATION (max 25 points)

• Discussion based on the written test: students have to explain how they solved each problem. Should the student fail to explain it sufficiently, the test results will not be accepted and will be classified by 0 points.

• Possible theoretic question.

• Possible simple problem to be solved straight away.

• The results achieved in the written tests in seminars may be taken into account within the oral examination.

FINAL CLASSIFICATION:

0-49 points: F

50-59 points: E

60-69 points: D

70-79 points: C

80-89 points: B

90-100 points: A

Course curriculum

Work placements

Aims

Specification of controlled education, way of implementation and compensation for absences

Recommended optional programme components

Prerequisites and corequisites

Basic literature

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

Recommended literature

Karásek J.: Matematika II (skriptum VUT)

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)

Thomas G.B., Finney R.L.: Calculus and Analytic Geometry (7th edition)

Elearning

**eLearning:**currently opened course

Classification of course in study plans

- Programme B-MET-P Bachelor's 1 year of study, summer semester, compulsory
- Programme B-ZSI-P Bachelor's
specialization STI , 1 year of study, summer semester, compulsory

specialization MTI , 1 year of study, summer semester, compulsory - Programme LLE Lifelong learning
branch CZV , 1 year of study, summer semester, compulsory

#### Type of course unit

Lecture

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Syllabus

Week 2: Higher-order partial derivatives, gradient of a function, derivative in a direction, first-order and higher-order differentials, tangent plane to the graph of a function in two variables.

Week 3: Taylor polynomial, local maxima and minima of functions in several variables.

Week 4: Relative maxima and minima, absolute maxima and minima.

Week 5: Functions defined implicitly.

Week 6: Double and triple integral, Fubini's theorem: calculation on normal sets.

Week 7: Substitution theorem, cylindrical a spherical co-ordinates.

Week 8: Applications of double and triple integrals.

Week 9: Curves and their orientations, first-type line integral and its applications.

Week 10: Second-type line integral and its applications, Green's theorem.

Week 11: Line integrals independent of the integration path, potential, the nabla and delta operators, divergence and curl of a vector field.

Week 12: Surfaces (parametric equations, orienting of a surface), first-type surface integral and its applications.

Week 13: Second-type surface integral and its applications, Gauss' theorem and Stokes' theorem.

Exercise

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Computer-assisted exercise

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Elearning

**eLearning:**currently opened course