Introduction to Calculus

Lecturer:

Tomáš Bílek, Josef Hekrdla

Tutor:

Tomáš Bílek, Josef Hekrdla

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:

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:

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	roomTRUTNOV Hekrdla J. 09:15–10:45 ODD WEEK (lecture parallel2) Sportovní objekty Trutnov roomT2:C3-132 Bílek T. Hekrdla J. 10:00–11:45 EVEN WEEK (lecture parallel1) Dejvice Posluchárna
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_162957 (compulsory course in the program)
• Elektrotechnika, energetika a management - Elektrotechnika a management_163134 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Komunikační technika_163439 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Multimediální technika_163458 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Aplikovaná elektronika_163524 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Síťové a informační technologie_163540 (compulsory course in the program)
• Elektrotechnika, energetika a management, před rozřazením do oborů (compulsory course in the program)
• Komunikace, multimedia a elektronika, před rozřazením do oborů (compulsory course in the program)
• Komunikace, multimédia a elektronika (compulsory course in the program)