Subject description - A0B01MA1

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A0B01MA1 Introduction to Calculus Extent of teaching:3+3
Guarantors:Sobotíková V. Roles:P,V Language of
teaching:
CS
Teachers:Sobotíková V. 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:

https://moodle.fel.cvut.cz/courses/A0B01MA1

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPKME1 Communication Technology P 1
BPKME2 Multimedia Technology P 1
BPKME5 Komunikace a elektronika P 1
BPKME3 Applied Electronics P 1
BPKME_BO Common courses P 1
BPKME4 Network and Information Technology P 1
BPOI_BO Common courses V 1
BPOI3 Software Systems V 1
BPOI2 Computer and Information Science V 1
BPOI1 Computer Systems V 1
BPEEM1 Applied Electrical Engineering P 1
BPEEM_BO Common courses P 1
BPEEM2 Electrical Engineering and Management P 1
BPSTMMI Manager Informatics V 1
BPSTMWM Web and Multimedia V 1
BPSTMSI Software Engineering V 1
BPSIT Common courses V 1
BPSTM_BO Common courses V 1
BPSTMIS Intelligent Systems V 1
BKSIT Common courses V 1
BSI(ECTS) Software Engineering V 1
BIS(ECTS) Intelligent Systems V 1
BWM(ECTS) Web and Multimedia V 1
BMI(ECTS) Manager Informatics V 1


Page updated 20.7.2018 17:49:08, semester: Z,L/2020-1, L/2019-20, L/2018-9, Z,L/2017-8, Z/2018-9, Z/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)