Syllabus
1. Sets and operations on sets, predicate logic. Sets of numbers. The supremum axiom. Sequences and their limits, accumulations points, countable and non-countable sets.
2. Function of one real variable, limit and continuity. One-to-one function. Composite function, parametrically given function. Elementary functions.
3. Primitive function, integration by parts and Theorem on Substitution; integration of elementary functions, especially rational ones. Solution to special ODEs.
4. Further properties of limits. Symbols o and O (small and capital o). Sequences and their properties: monotone sequences and their limit. Bolzano-Cauchy Theorem.
5. Properties of continuous functions on a closed interval. Mean Value Theorem. L'Hospital's Rule. Sketching of the graph of a function using derivatives. Convexity and concavity. Taylor polynomial and Taylor formula.
7. Riemann and Newton integral. Integral with changing upper limit. Connection between primitive function and Riemann integral. Mean Value Theorem of the integral calculus.
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.