Introduction to Calculus

Lecturer:

Paola Vivi

Tutor:

Paola Vivi

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	roomZ4:B2-326 Vivi P. 13:30–15:15 ODD WEEK (lecture parallel1) Zikova ulice Konzultační místnostroomZ4:B2-326 Vivi P. 15:15–17:00 ODD WEEK (lecture parallel1 parallel nr.101) Zikova ulice Konzultační místnost
Tue
Fri
Thu	roomZ4:B2-326 Vivi P. 13:30–15:15 (lecture parallel1) Zikova ulice Konzultační místnostroomZ4:B2-326 Vivi P. 15:15–17:00 (lecture parallel1 parallel nr.101) Zikova ulice Konzultační místnost
Fri

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Electrical Engineering, Power Engineering and Management - Applied Electrical Engineering (compulsory course in the program)
• Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (compulsory course in the program)
• Communications, Multimedia and Electronics - Communication Technology (compulsory course in the program)
• Communications, Multimedia and Electronics - Multimedia Technology (compulsory course in the program)
• Communications, Multimedia and Electronics - Applied Electronics (compulsory course in the program)
• Communications, Multimedia and Electronics - Network and Information Technology (compulsory course in the program)
• Electrical Engineering, Power Engineering and Management (compulsory course in the program)
• Communications, Multimedia and Electronics (compulsory course in the program)