Brief description of the course
The set of real numbers, its continuity. The concept of a function. Limit of a function, its properties and conditions for existence. Continuous functions, their properties. Functions continuous on a closed interval. Derivative of a function, its properties, interpretations and conditions for existence. Differentiability and differential of a function. Higher-order derivatives and differentials. Parametric functions, their existence and differentiation. Mean value theorems in differential calculus, their applications to the finding of limits and treating of functions. Applications in geometry. Taylors formula.
Attending lectures is a prerequisite of the learning process.
Learning outcomes in the course
Upon completing the course the student...
After passing this course the student
- knows main notions of differential calculus;
- is familiar with the main properties, relations and theorems of this course
- is familiar with some proof methods and is able to use them for some theorems of this course
- is able to use and apply methods taught in a subject in order to solve exercises.