Introduction to Calculus
Code  Completion  Credits  Range  Language 

AE0B01MA1  Z,ZK  8  3+3 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

This is an introductory course to calculus of real functions of one variable. In the first part we study limits and continuity of functions, derivative and its geometrical meaning, graphing of functions. Then we define the indefinite integral, and discuss basic integration methods, the definite integral and its applications. We conclude with an introduction to Laplace transform and its use in solving differential equations.
 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 (using sums). NewtonLeibniz formula.
9.Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10.Improper integral.
11.Laplace transform.
12.Basic properties of direct and inverse Laplace transform.
13.Using Laplace transform to solve differential equations.
 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 (using sums). NewtonLeibniz formula.
9.Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10.Improper integral.
11.Laplace transform.
12.Basic properties of direct and inverse Laplace transform.
13.Using Laplace transform to solve differential equations.
 Study Objective:
 Study materials:

1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994
2. P. Pták: Calculus II. ČVUT Praha, 1997.
 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:

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