*Conducted in terms:*2020Z, 2021Z

*Erasmus code:*11.1

*ECTS credits:*3

*Language:*Polish

# Mathematics 1000-111MAT

We will start the lecture from the description of basic mathematical notions such as sets, numbers, relations, functions. Next, we will describe basic types of functions: linear, exponential and logarythmic as well as logarithms and its applications. The main part on the lecture will be devoted to mathematical analysis. We will define the notion of limit (in the context of sequences and functions), continuity and differentiability of one variable functions. We will try to understand geometrical and physical interpretations of derivative. Next we will describe an extremum and study the dependence between extrema and convexity (concavity) of the function. The theoretical part of the lecture will end with the description of primitive function and the notion of integral and its geometrical interpretation. In the last part of the lecture we will focus on mathematical modelling of biological phenomena. Therefore, it will be necessary to introduce the notion of ordinary differential equations. On the basis we will study some models of population dynamics (equation of Malthus, logistic equation, competition, predation, symbiosis). We will introduce some basic notions of the probability theory and define Markov chains and its applications for models of evolution.

## Type of course

## Course coordinators

## Assessment criteria

The final note will be based on the result of the written exam and students' work during classes.

## 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:

- Biotechnology, part-time (evening) first-cycle
- Biology, full-time first cycle studies
- Biotechnology, full-time first-cycle studies
- Environmental conservation, full-time first-cycle studies

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