Syllabus
1. Sets and operations on sets, predicate logic.
2. Sets of numbers. The supremum axiom. Sequences and their limits, accumulations points, countable and non-countable sets. Bolzano-Cauchy Theorem.
3. Function of one real variable, limit and continuity. One-to-one function. Composite function, parametrically given function. Elementary functions.
4. Derivative and differential of a function of one real variable. Arithmetic on derivatives.
5. Primitive function, integration by parts and Theorem on Substitution; integration of elementary functions, especially rational ones. Solution to special ODEs.
6. Properties of continuous functions on a closed interval. , Mean Value Theorem. Sketching of the graph of a function using derivatives. Convexity and concavity. L'Hospital's Rule, symbols o and O (small and capital o), Taylor polynomial and Taylor formula.
7. Definite (Riemann, Newton) integral. Integral with changing upper limit. Connection between primitive function and definite integral. Mean Value Theorem of the integral calculus. Applications: lenght of a curve, volume of a rotational body, surface in polar coordinates, moments.
Annotation
First part of the basic course of mathematics for the students of general physics (bachelor study). The program consists of basics on differential and integral calculus, together with theoretical background.