*Conducted in term:*2022Z

*Erasmus code:*11.1

*ISCED code:*0541

*ECTS credits:*9

*Language:*Polish

*Organized by:*Faculty of Physics

*Related to study programmes:*

# Analysis I 1100-1AF12

1. Elements of logic and set theory.

- Basic symbols and notation of logic and set theory.

- Mathematical induction.

- Equivalence relations.

- Functions and graphs.

2. Convergence

- Axioms of the real number system.

- Least upper bound and greatest lower bound.

- Sequences of real numbers.

- Metric spaces.

- Closed sets, open sets, connected sets.

- Compactness.

3. Differential calculus in one variable.

- Taylor's formula.

- De l'Hospital rule.

- Convex functions.

- The primitive.

- Analysis of functions.

- Series.

- Radius of convergence of a power series.

- Power series expansions of elementary functions.

- The Riemann integral of functions of one variable.

## Main fields of studies for MISMaP

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## 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:

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*localization and schedules* of classes), might be available in the USOSweb system: