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) | 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-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 |
| ||||||||||
| 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. Additionally:
- A.C.M. Van Rooij, W.H. Schikhof, Α second course on real functions, Cambridge University Press.