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School of Science
Department of Mathematics
|Level of Studies||
Topics on Real Functions
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|Is the Course Offered to Erasmus Students||
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
The plan of the course is the achievement by the undergraduate student of special theoretical background in the theory of real functions.
The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in the theory of real functions.
Monotone functions-continuity, functions of bounded variation, Fς and Gd sets, sets of measure zero, Lebesgue's theorem (every monotone function is differentiable almost everywhere), Darboux continuous functions-definitions, properties, equivalent characterizations, criteria, Semicontinuous functions, differentiability of the Riemann integral of a function, Baire classes, Borel measurable functions, analytic sets-characterizations, connections with Borel sets-related theory, Lebesgue and Stieltjes integrals.
Teaching and Learning Methods - Evaluation
|Use of Information and Communications Technology||-|
|Student Performance Evaluation||
Written examination at the end of the semester.
- A.C.M. Van Rooij, W.H. Schikhof, Α second course on real functions, Cambridge University Press.