Apr 3, 2020   1:06 a.m. Richard

# Course syllabus B-MAT2I - Mathematics 2 (FEEIT - WS 2019/2020)

Information sheet          ECTS          Syllabus

Slovak          English

University: Slovak University of Technology in Bratislava
Faculty: Faculty of Electrical Engineering and Information Technology
Course unit code: B-MAT2I
Course unit title: Mathematics 2
Mode of delivery, planned learning activities and teaching methods:
 lecture 2 hours weekly (on-site method) seminar 2 hours weekly (on-site method)

Credits allocated: 6

Recommended semester/trimester: -- item not defined --
Level of study: 1.
Prerequisites for registration: passed Mathematics 1 (B-MAT1I)

Assesment methods:
Written tests during the semester for 30 points. For credit at least 50% of total is needed.
Final exam at the end of semester for 70 points.
Sum of all points determines the final evaluation.

For evaluation A at least 92 points is needed,for evaluation B at least 83 points is needed, for evaluation C at least 74 points is needed, For evaluation D at least 65 points is needed,for evaluation E at least 56 points is needed.

Learning outcomes of the course unit:
After completing this course, students should have developed an understanding of the fundamental concepts of multivariable calculus and basic skills allowing them to work with the concepts derivatives and integrals.

•An understanding of the gradient, directional derivatives, and linear approximation.
•The ability to compute derivatives using the chain rule or total differentials.
•The ability to solve optimization problems involving several variables, with or without constraints.
•The ability to compute double integrals. An understanding of the physical interpretation of these integrals.
•The ability to set up and compute multiple integrals in rectangular and polar coordinates.
•An understanding of change of variables in multiple integrals.

Course contents:
1. Vector space. Representation of functions of two and three variables.
2. Limits and continuity of a function of several variables.
3. Partial derivatives, directional derivative, gradient. The chain rule.
4. Tangent plane, differential and differentility.
5. Local extrems of the function of several variables.
6. second partial derivatives and second differential.
7. Taylor's theorem and expansion of the function of two variables. Applications.
8. Optimization of constrained functions.
9. The notion of double integral. Definition and basic properties.
10. Repeated integration, Fubini theorem.
11. Substution in double integrals. Transformation to polar coordinates.
12. Applications.

Basic:
 SATKO, L. -- ŠULKA, R. Matematická analýza II: Diferenciálny a integrálny počet funkcie viac premenných. Bratislava : STU v Bratislave, 1995. 160 p. ISBN 80-227-0735-X. MORAVSKÝ, L. -- MORAVČÍK, J. -- ŠULKA, R. Matematická analýza 2. Bratislava : Alfa, 1992. 552 p. ISBN 80-05-00934-8. BRABEC, J. -- HRŮZA, B. Matematická analýza II. Praha : SNTL, 1986. 579 p. MARKO, Ľ. Matematická analýza online.  [online]. 2003. URL: http://www.fei.stuba.sk/~ marko.

Recommended:
 Edwards, C.H., Penney, D.E.: Calculus and Analytic Geometry, (3rd edition), Prentice Hall International, New York 1990 Glyn, J.: Modern engineering mathematics, Addison Wesley, 2008

Language of instruction: slovak or english

Notes:
As a prerequisity Mathematics 1 is neeeded

Courses evaluation:
Assessed students in total: 1280

ABCDEFX
5,2 %6,5 %12,0 %20,0 %43,0 %13,3 %
Name of lecturer(s): RNDr. Mária Kečkemétyová, PhD. (examiner, instructor, lecturer)
doc. RNDr. Boris Rudolf, PhD. (lecturer, person responsible for course) - slovak, english

Last modification: 6. 5. 2019
Supervisor: doc. RNDr. Boris Rudolf, PhD. and programme supervisor

Last modification made by RNDr. Marian Puškár on 05/06/2019.

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