Subject description - AE0B01MA1

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AE0B01MA1 Introduction to Calculus Extent of teaching:3+3
Guarantors:  Roles:P,V Language of
teaching:
EN
Teachers:  Completion:Z,ZK
Responsible Department:13101 Credits:8 Semester:Z

Anotation:

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.

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 (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.

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 (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.

Literature:

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

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

Webpage:

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

Subject is included into these academic programs:

Program Branch Role Recommended semester
BEEEM1 Applied Electrical Engineering P 1
BEEEM_BO Common courses P 1
BEEEM2 Electrical Engineering and Management P 1
BEKME1 Communication Technology P 1
BEKME5 Komunikace a elektronika P 1
BEKME_BO Common courses P 1
BEKME4 Network and Information Technology P 1
BEKME3 Applied Electronics P 1
BEKME2 Multimedia Technology P 1
BEOI1 Computer Systems V 1
BEOI_BO Common courses V 1
BEOI3 Software Systems V 1
BEOI2 Computer and Information Science V 1


Page updated 17.6.2019 14:52:47, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)