CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

# Introduction to Calculus

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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.

http://math.feld.cvut.cz/vivi/AE0B01MA12010.pdf

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). Newton-Leibniz 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). Newton-Leibniz 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: