Topics in Functions of One Variable (MAE515): Διαφορά μεταξύ των αναθεωρήσεων

Τελευταία αναθεώρηση της 18:21, 17 Αυγούστου 2024

Ελληνική Έκδοση
Undergraduate Courses Outlines
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Department of Mathematics
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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΕ515
Semester	5
Course Title	Topics in Functions of One Variable
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)	See eCourse, the Learning Management System maintained by the University of Ioannina.

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 - points of continuity, functions of bounded variation, sets of measure zero, Lebesgue's theorem (every monotone function is differentiable almost everywhere), Darboux continuous functions-definitions, properties, equivalent characterizations, convex functions, semicontinuous functions, continuity points of Riemann integrable functions, Baire classes, Borel measurable functions, analytic sets-characterizations, connections with Borel sets-related theory, Lebesgue integral, Stieltjes integral.

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

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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

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-* [[Ειδικά Θέματα Απειροστικού Λογισμού (MAE752)|Ελληνική Έκδοση]]
+* [[Θέματα Συναρτήσεων Μίας Μεταβλητής (MAE515)|Ελληνική Έκδοση]]
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 ! Course Code
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-ΜΑΕ752
+ΜΑΕ515
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-Special Topics in Infinitesimal Calculus
+Topics in Functions of One Variable
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 === 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.
+Monotone functions - points of continuity, functions of bounded variation, sets of measure zero, Lebesgue's theorem (every monotone function is differentiable almost everywhere), Darboux continuous functions-definitions, properties, equivalent characterizations, convex functions, semicontinuous functions, continuity points of Riemann integrable functions, Baire classes, Borel measurable functions, analytic sets-characterizations, connections with Borel sets-related theory, Lebesgue integral, Stieltjes integral.
 === Teaching and Learning Methods - Evaluation ===
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