Topics in Functions of One Variable (MAE515)
General
School |
School of Science |
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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. |
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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 | ||||||||||
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Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
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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.