*Conducted in terms:*2020Z, 2021Z

*Erasmus code:*11.1

*ISCED code:*0541

*ECTS credits:*6.5

*Language:*Polish

*Organized by:*Faculty of Mathematics, Informatics, and Mechanics

*Related to study programmes:*

# Calculus 1000-711RRC

Basic notions of propositional calculus and first-order logic. Basics of set theory. Polynomials with real and complex roots. Polynomial remainder theorem (little Bézout's thm). Rational functions. Elementary functions: exponentials, logarithms, trigonometric and inverse trigonometric functions.

Limit of a sequence and the sum of an infinite series.

Limits and continuity of functions.

The notion of the derivative, geometrical and mechanical meaning. Basics of calculus of one variable. The mean value theorem, a maximum and a minimum, Taylor's theorem, an indeterminate form. The local behavior of the function.

An antiderivative and the definite integral, Newton-Leibniz formula. The geometrical meaning of integration. Integration techniques.

## Type of course

## Course coordinators

## Learning outcomes

At the end of the course student

1) knows and understands: the most common elementary functions, notion of the limit of a sequence and of a function,

2) is able to calculate the routine limits, derivatives, integrals (also using the Taylor expansion of the function).

## Notes

Term 2020Z:
None |
Term 2021Z:
None |

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: