Mathematics I

The aim of the course is to familiarize students with the basic concepts of mathematical analysis, necessary for further studies. Functions of single real variable. Repetition of fundamental functions and their properties. Determining the domains and ranges of functions, describing their properties. Numerical sequences and their limits. Limits and continuity of functions. Differential and integral calculus of single variable functions.

Students know graphs and properties of elementary functions, the concept of derivative and differential of one variable functions. Students have knowledge on indefinite and definite integrals of one variable functions. Students can calculate derivatives of functions of one variable and use them to solve geometric, optimization and approximate calculation problems. Students are able to calculate indefinite integrals of one variable functions. Students are able to calculate definite integrals and improper integrals of one variable functions as well as use them to solve geometric problems. Students understand to an even greater extent the need for continuous education, especially in the field of modern mathematics methods used in technology. Students know the limits of their own knowledge and are aware of the need for systematic work and further education.