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.
Language of instruction
Number of ECTS credits
Mode of study
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
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
Satunino, L.S., Hille, E., Etgen, J.G.: Calculus: One and Several Variables, Wiley 2002
Sneall D.B. - Hosack J.M.: Calculus, An Integrated Approach
Thomas G. B.: Calculus (Addison Wesley, 2003)
Thomas G.B. - Finney R.L.: Calculus and Analytic Geometry, 7th edition
Recommended reading
Eliáš J., Horváth J., Kajan J.: Zbierka úloh z vyššej matematiky I, II, III, IV (Alfa Bratislava, 1985)
Karásek J.: Matematika II (skriptum VUT)
Mezník I. - Karásek J. - Miklíček J.: Matematika I pro strojní fakulty (SNTL 1992)
Rektorys K. a spol.: Přehled užité matematiky I,II (SNTL, 1988)
Thomas G.B., Finney R.L.: Calculus and Analytic Geometry (7th edition)
Elearning
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
Teacher / Lecturer
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
Teacher / Lecturer
Syllabus
Computer-assisted exercise
Teacher / Lecturer
Syllabus
Elearning