Calculus
Code  Completion  Credits  Range  Language 

AE4B01MA2  Z,ZK  8  4+2 
 Prerequisite:
 Linear Algebra (AE0B01LAG)
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

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.
 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.
 Syllabus of lectures:

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. NewtonLeibniz 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.
 Syllabus of tutorials:

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. NewtonLeibniz 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.
 Study Objective:
 Study materials:
 Note:
 Further information:
 http://math.feld.cvut.cz/vivi/
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Cybernetics and Robotics  Robotics (elective course)
 Cybernetics and Robotics  Senzors and Instrumention (elective course)
 Cybernetics and Robotics  Systems and Control (elective course)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering (elective course)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (elective course)
 Communications, Multimedia and Electronics  Communication Technology (elective course)
 Communications, Multimedia and Electronics  Multimedia Technology (elective course)
 Communications, Multimedia and Electronics  Applied Electronics (elective course)
 Communications, Multimedia and Electronics  Network and Information Technology (elective course)
 Open Informatics  Computer Systems (compulsory course in the program)
 Open Informatics  Computer and Information Science (compulsory course in the program)
 Open Informatics  Software Systems (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management (elective course)
 Communications, Multimedia and Electronics (elective course)
 Cybernetics and Robotics (elective course)
 Open Informatics (compulsory course in the program)
 Communications, Multimedia and Electronics  Communications and Electronics (elective course)