Topics in Functions of One Variable (MAE515)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΕ814
Semester	8
Course Title	Topics on Real Functions
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	-

Learning Outcomes

Learning outcomes	The plan of the course is the achievement by the undergraduate student of special theoretical background in the theory of real functions.
General Competences	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.

Syllabus

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

Delivery	Face-to-face
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Independent study 78 Exercises solutions 33 Course total 150
Student Performance Evaluation	Written examination at the end of the semester.

Attached Bibliography

• A.C.M. Van Rooij, W.H. Schikhof, Α second course on real functions, Cambridge University Press.