Introduction To Functional Analysis(MAT452)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT452 | Introduction To Functional Analysis | 7 | 4 | 0 | 0 | 4 | 8 |
| Prerequisites | MAT201, MAT261, MAT262 |
| Admission Requirements | MAT201, MAT261, MAT262 |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Serap GÜRER serapgurer@gmail.com (Email) |
| Assistant | |
| Objective | The objective of this course is to study the the basic tools for the functional anlysis |
| Content |
Banach spaces, Hilbert spaces, Hahn Banach theorem integrability, completeness of Lp spaces Applications of functional analysis. |
| Course Learning Outcomes | |
| Teaching and Learning Methods | Course and Recitation Hours |
| References | Introductory Functional Analysis and Applications, Erwin Kreyszig |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Metric Spaces: Complete spaces, compactness |
| 2 | Definitions and examples of Banach spaces. Continuous and integrable function spaces |
| 3 | Banach spaces, compactness and finite dimension, Ascoli’s theorem |
| 4 | Duality in Banach spaces |
| 5 | Definitions and examples of Hilbert spaces. |
| 6 | Orthogonality and projection. Riesz–Fischer theorem |
| 7 | Midterm |
| 8 | Fundamental theorem of functional analysis: Zorn's Lemma, Hahn Banach's Theorem |
| 9 | Fundamental theorem of functional analysis: Zorn's Lemma, Hahn Banach's Theorem |
| 10 | Homework |
| 11 | Lp spaces, measurement theory and definition of Lp spaces |
| 12 | Lp spaces as Banach spaces, Density in Lp spaces |
| 13 | Applications of Functional Analysis: Fourier Transformation and Applications |
| 14 | Applications of functional analysis: Sobolev spaces and their properties |
Practice Topics
| Week | Weekly Contents |
|---|---|
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Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 1 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 2 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 2 | 30 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 3 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 14 | 2 | 28 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Final Examinations (including preparation) | 1 | 20 | 20 |
| Quiz | 2 | 6 | 12 |
| Total Workload | 126 | ||
| Total Workload / 25 | 5.04 | ||
| Credits ECTS | 5 | ||