Introduction to Calculus
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| A0B01MA1 | Z,ZK | 8 | 3+3s | Czech |
- Lecturer:
- Veronika Sobotíková (gar.), Josef Hekrdla
- Tutor:
- Veronika Sobotíková (gar.), Lucie Augustovičová, Vojtěch Bartík, Barbora Benešová, Externista Bunčák, Externista Exnerová, Lidmila Gabrielová, Josef Hekrdla, Miluše Hyánková, Rastislav Oľhava, Karel Pospíšil, Ladislav Průcha, Externista Soudský, Robert Švarc, Jakub Tichý, Externista Vlasák
- Supervisor:
- Department of Mathematics
- Synopsis:
-
It is an introductory course to calculus of functions of one variable. It starts with limit and continuity of functions, derivative and its geometrical meaning and properties, graphing of functions. Then it covers indefinite integral, basic integration methods and integrating rational functions, definite integral and its applications. It concludes with introduction to Laplace Transformation.
- Requirements:
- 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:
- Time-table for winter semester 2011/2012:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri - Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Elektrotechnika, energetika a management - Aplikovaná elektrotechnika (compulsory course in the program)
- Elektrotechnika, energetika a management - Elektrotechnika a management (compulsory course in the program)
- Komunikace, multimedia a elektronika - Komunikační technika (compulsory course in the program)
- Komunikace, multimedia a elektronika - Multimediální technika (compulsory course in the program)
- Komunikace, multimedia a elektronika - Aplikovaná elektronika (compulsory course in the program)
- Komunikace, multimedia a elektronika - Síťové a informační technologie (compulsory course in the program)
- Komunikace, multimedia a elektronika - před rozřazením do oborů (compulsory course in the program)
- Elektrotechnika, energetika a management - před rozřazením do oborů (compulsory course in the program)
- Komunikace, multimédia a elektronika - Komunikace a elektronika (compulsory course in the program)