Syllabus
Main topics:
- The notion of the limit of a function (proper, improper, at a real point and at infinity), its calculation, "undetermined" expressions
- Continuity of a function at a point and on an interval, properties of continuous functions, the relation of the notions continuity and limit
- Derivative, its physical and geometrical interpretation, its calculation (especially for compound and inverse function), mean value theorems, l'Hospital rule.
The meaning of higher order derivatives for the behaviour of a function and the shape of its graph.
Annotation
The aim of the course is to introduce the students to the basic notions of the differential calculus (the notions of limit, continuity, derivative), to lead them to a deeper understanding of limit transition as a tool suitable to deal with real dynamical processes and to train them in practical calculations with limits and derivatives. Special attention will be given to the use of the notions and techniques of differential calculus in the study of elementary functions and in the physical applications.