| Learning Outcomes |
PO |
MME |
| The students who succeeded in this course: |
|
|
| LO-1 |
To teach the basic concepts of functional analysis, |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
|
Examination
|
| LO-2 |
To give some applications of functional analysisFonksiyonel |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
|
|
| LO-3 |
To prepare the students to higher level functional analysis lectures. |
PO-
|
|
PO: Programme Outcomes
MME:Method of measurement & Evaluation |
| Course Contents |
| Normed spaces, l_p , l_q and C[a,b] spaces, norm of operators, Weierstrass approximation theorem, Hahn-Banach theorem, uniform boundedness theorem, inner product spaces, Riesz-Freched Theorem, , Gram-Schmidd theoem, operators in inner product spaaces |
| Weekly Course Content |
| Week |
Subject |
Learning Activities and Teaching Methods |
| 1 |
Definations of norm and normed spaces |
Problems and solutions |
| 2 |
The spaces l_p, l_q and C[a,b] |
Problems and solutions |
| 3 |
Dual of normed space |
Problems and solutions |
| 4 |
Isomorphisms and isometries on normed spaces |
Problems and solutions |
| 5 |
Linear operators on normed spaces |
Problems and solutions |
| 6 |
Bounded linear operators |
Problems and solutions |
| 7 |
Finite dimentional normed spaces |
Problems and solutions |
| 8 |
mid-term exam |
|
| 9 |
Banach spaces |
Problems and solutions |
| 10 |
Weierstrass approximation theorem |
Problems and solutions |
| 11 |
Hahn-Banach theorem |
Problems and solutions |
| 12 |
Uniform boundedness theorem, open mapping theoremand closed graphic theorem |
Problems and solutions |
| 13 |
Inner product spaces and Hilbert spaces . |
Problems and solutions |
| 14 |
Properties of inner product space, orthogonal complement and direct sum . |
Problems and solutions |
| 15 |
Functionals and Riesz Representation of functionals |
Problems and solutions |
| 16 |
final exam |
|
| Recommend Course Book / Supplementary Book/Reading |
| 1 |
Introduction to Hilbert Spaces with Applications, Lokenath Debnath and Piotr Mikusinski, Acedemic Press1999 |
| 2 |
Firs course in Functional Analysis, Casper Goffman and George Pedrick, Chelsa Publishing Campany, |
| Required Course instruments and materials |
| Lecuture notes and textbooks |
