Introduction to Real Analysis

Description

Real numbers - Countable and uncountable sets - Sequences and series - permutations of series - representations of real numbers - The Cantor set and Cantor’s function - Special classes of functions (monotone, bounded variation, absolutely continuous, convex) - Sequences and series of functions - uniform convergence and applications - nowhere differentiable continuous functions - space filling curves - equicartinuity - Azzela’s-Ascoli’s theorem - Weierstrass approximation theorem - Lebesque’s measure.

Course Coordinators

Books: 
- Πραγματική Ανάλυση του Π. Ξενικάκη.
Aρχές Μαθηματικής Ανάλυσης του W. Rudin
Semester: 
Units: 
3
Credit Units (ECTS): 
5.5
Hours: 
3ώρες
ID: 
0207
Course Type: 
X