Harmonic Analysis (MAE718)
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- Undergraduate Courses Outlines
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE718 |
| Semester |
7 |
| Course Title |
Harmonic Analysis |
| 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 (In English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The aim of the course is the achievement by the undergraduate student of the theoretical background in the theory of Fourier series |
|---|---|
| General Competences |
The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in Harmonic Analysis. |
Syllabus
Trigonometric polynomials, partial sums of the Fourier series of a function, Bessel's inequality, Lemma Riemann-Lebesgue, Parseval's identity for Riemann integrable functions, complex Riemann integrable functions defined on an interval, Fourier coefficients and Fourier series, the Dirichlet kernel, criteria for uniform convergence of the Fourier series, convolution of functions and approximations to the identity, Fejer kernel, theorem of Fejer, Poisson kernel, Abel summability of the Fourier series, applications.
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. Books and other resources, not provided by Eudoxus:
- Yitzhak Katznelson, An Introduction to Harmonic Analysis, Dover Edition.
- Elias M. Stein, Rami Shakarchi, Fourier Analysis, An Introduction, Princeton University Press.