Introduction to Calculus and Linear Algebra 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Requirements:

Syllabus of lectures:

1) Sets and mappings, supremum and infimum.

2) Functions and their properties.

3) Limits of functions and sequences.

4) Continuity.

5) Derivative of a function, basic properties.

6) Differential calculus of one variable, monotonicity, convexity, local and global extrema, asymptotes, tangent to a graph of a function.

7) Applications of differential calculus.

8) Indefinite integral, primitive functions, integration per parts, substitution, advanced techniques of integration

9) Definite integral, Newton formula.

10) Applications of integral calculus.

11) Infinite series

12) Systems of linear equations

13) Vectors and matrices

14) Vector spaces, basis and dimension, linear dependence and independence

15) Linear mapping

Syllabus of tutorials:

Study Objective:

Goals: Knowledge:

Elementary notions of mathematical analysis of the differential and integral calculus of functions of one real variable. Basics of linear algebra.

Abilities:

Understanding the basics of mathematical logic, mathematical analysis and linear algebra.

Requirements:

Key words: Differential calculus, integral calculus, functions of one

real variable, limits, extremes of functions, systems of linear equations, matrices, vector spaces.

Study materials:

Key references:

[1] Calculus, One Variable, S.L.Salas, Einar Hille, John Wiley and Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1990 (6th edition), ISBN 0-471-51749-6

[2] Essential Calculus, Stewart J.,

Brooks Cole, 2006.

[3] Principles of Mathematical Analysis, Rudin W., New York: McGraw-Hill, 1987 (3rd edition).

[4] Linear Algebra with Applications, Nicholson W. K.,

Boston: PWS Publishing Company, 1993.

[5] Linear Algebra. A Modern Introduction. Poole D., Brooks/Cole, Thomson Learning 2003.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: