Topics in Functions of One Variable (MAE515)

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General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

ΜΑΕ515

Semester

7

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-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, Semicontinuous functions, continuity points of Riemann integrable functions, Baire classes, Borel measurable functions, analytic sets-characterizations, connections with Borel sets-related theory, Lebesgue 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.