Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
Roles:P, V Extent of teaching:28+6
Department:13101 Language of teaching:CS
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:8
Tutors:  Semester:L

Anotation:

This is an introductory course to calculus. In the first part we study limits, continuity and derivative of real functions of one variable. Then we define the indefinite integral, discuss basic integration methods, the definite integral and its applications. We extend the discussion to real functions of more variables, partial derivatives and multiple integrals. We conclude with the study of real numerical series.

Course outlines:

 1 Elementary functions. Limit and continuity of functions. 2 Derivative of functions, its properties and applications. 3 Mean value theorem. L'Hospital's rule. 4 Limit of sequences. Taylor polynomial. 5 Local and global extrema and graphing functions. 6 Indefinite integral, basic integration methods. 7 Integration of rational and other types of functions. 8 Definite integral. Newton-Leibniz formula. 9 Improper integral.Applications of integrals. 10 Sequences, introduction to series. 11 Functions of two or more variables. Partial derivatives. 12 Maximum and minimum for functions of two variables. 13 Duble integrals.

Exercises outline:

 1 Elementary functions. Limit and continuity of functions. 2 Derivative of functions, its properties and applications. 3 Mean value theorem. L'Hospital's rule. 4 Limit of sequences. Taylor polynomial. 5 Local and global extrema and graphing functions. 6 Indefinite integral, basic integration methods. 7 Integration of rational and other types of functions. 8 Definite integral. Newton-Leibniz formula. 9 Improper integral.Applications of integrals. 10 Sequences, introduction to series. 11 Functions of two or more variables. Partial derivatives. 12 Maximum and minimum for functions of two variables. 13 Duble integrals.

Literature:

 1 J. Tkadlec: Diferenciální a integrální počet funkcí jedné proměnné. ČVUT Praha, 2004. 2 L. Průcha: Řady. ČVUT Praha, 2005. 3 Hamhalter, J., Tišer, J.: Diferenciální počet funkcí více proměnných, ČVUT Praha, 2005. 4 Habala, P.: Math Tutor, http://math.feld.cvut.cz/mt/

Requirements:

In order to obtain the certificate of attendance, students are required to actively participate in the laboratory class, hand in the assigned homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate ("zapocet") are allowed to take the exam.

Webpage:

http://math.feld.cvut.cz/habala/teaching/ma2.htm

Subject is included into these academic programs:

 Program Branch Role Recommended semester BKEEM1 Applied Electrical Engineering V 2 BKEEM_BO Common courses V 2 BKEEM2 Electrical Engineering and Management V 2 BKOI1 Computer Systems P 2 BKOI_BO Common courses P 2 BKOI3 Software Systems P 2 BKOI2 Computer and Information Science P 2 BKKYR1 Robotics V 2 BKKYR_BO Common courses V 2 BKKYR3 Systems and Control V 2 BKKYR2 Sensors and Instrumentation V 2 BKKME1 Communication Technology V 2 BKKME_BO Common courses V 2 BKKME4 Network and Information Technology V 2 BKKME3 Applied Electronics V 2 BKKME2 Multimedia Technology V 2 BIS(ECTS)-D Intelligent Systems V 2 BKSTMWM Web and Multimedia V 2 BKSTMSI Software Engineering V 2 BKSTMMI Manager Informatics V 2 BKSTMIS Intelligent Systems V 2 BKSTM_BO Common courses V 2 BSI(ECTS)-D Software Engineering V 2 BWM(ECTS)-D Web and Multimedia V 2 BMI(ECTS)-D Manager Informatics V 2

 Page updated 19.1.2021 17:54:11, semester: Z/2020-1, L/2021-2, L/2020-1, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)