Mathematics 1

Lecturer:

František Bubeník (gar.)

Tutor:

František Bubeník (gar.), Ondřej Zindulka

Supervisor:

Department of Mathematics

Synopsis:

The course is an introduction to differential calculus of functions of one variable and linear algebra. It deals with sets, mappings, sequences, elementary functions, real analysis, derivatives, extreme values, vector spaces, matrix algebra, systems of linear equations, applications and essential mathematical methods. Applications are taken from a range of engineering areas allowing to see mathematics in action by solving relevant problems. The use of computers is a focus throughout the course.

Requirements:

none

Syllabus of lectures:

1. Sequences.

2. Functions of a real variable. Composite and inverse functions. Elementary functions.

3. Limits and continuity. Weierstrass's and Bolzano's theorems.

4. Derivatives and their applications.

5. Properties of functions. Monotony. Points of inflection. Asymptotes.

6. Extreme values.

7. Taylor's theorem. Approximate roots of nonlinear equations.

8. Vector spaces.

9. Matrices. Gaussian elimination.

10. Systems of linear equations. Solvability.

11. Matrix operations. Inverse matrices. Matrix equations.

12. Determinants. Cramer's rule.

13. Topics in analytic geometry in 3D-space.

14. Analytical methods of geometric problems in 3D-space.

Syllabus of tutorials:

Study Objective:

Students are able to solve fundamental problems of linear algebra, analytic geometry in the plane and space and differential calculus of functions of one variable.

Study materials:

Bubeník F.: Mathematics for Engineers, Vydavatelství ČVUT, 1997. Bubeník F.: Problems to Mathematics for Engineers, Vydavatelství ČVUT, 1999. Rektorys K. et al.: Applied Mathematics, Praha, Prometheus 2000.

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	roomTH:B-368 Zindulka O. 13:00–15:50 (lecture parallel1 parallel nr.139) Thákurova 7 (FSv-budova A) B368
Fri	roomTH:C-202 Bubeník F. 10:00–11:50 (lecture parallel1) Thákurova 7 (FSv-budova A) C202
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: