Introduction to Real Numbers: Axioms of order, sets of natural, integer, and rational numbers, axiom of completeness, countable sets, topology of IR, inequalities. Sequences of Real Numbers: Properties of convergence, monotonic and divergent sequences, subsequences, basic sequences, applications. Series of Real Numbers: Convergence, convergence criteria, decimal representation of real numbers. Limit–Continuity: Definitions and basic theorems, uniform continuity. Derivative: Rolle s theorem, mean value theorem, theorems of monotonicity, extrema, convex functions. Elementary functions and their inverses, Taylor polynomial, Taylor series, Mclaurin formula. The indefinite Integral: Integration methods: analysis into a sum of simple fractions, integrals of non-rational functions. The definite integral: Riemann integral, basic theorems, integrability of continuous and monotonic functions, applications. Generalized Integrals: Definitions of generalized integrals of a , b kind and mixed, convergence criteria, the functions Γ and Β.
- Teacher: Βασίλειος Κανελλόπουλος
ECTS : 6
Language : el