| Code |
Course Name |
Language |
Type |
| MAT 288E |
Real Analysis I |
English |
Compulsory |
| Local Credits |
ECTS |
Theoretical |
Tutorial |
Laboratory |
| 4 |
6 |
4 |
0 |
0 |
| Course Prerequisites and Class Restriction |
| Prerequisites |
MAT 102 MIN DD
or MAT 102E MIN DD
or MAT 104 MIN DD
or MAT 104E MIN DD
or MAT 188 MIN DD
or MAT 211 MIN DD
or MAT 188E MIN DD
or MAT 213 MIN DD
or MAT 211E MIN DD
or MAT 213E MIN DD
|
| Class Restriction |
None |
| Course Description |
| Real numbers, Normed vector spaces. Finite dimensional real vector spaces. Young’s, Hölder’s and Minkowski’s inequalities.
Metric spaces. Sequences in metric spaces. Convergence and boundedness. Cauchy sequences and completeness. Topology
of Metric spaces: open and closed sets. Compactness. Heine-Borel Theorem. Real valued continuous functions on metric
spaces and their metric structure. Continuity and uniform continuity. Lipschitz continuity. Derivatives. Normed spaces
C^k[a,b], l^p and L^p and their duals. Hilbert spaces. Sequences and series of real valued functions on metric spaces. The
Stone- Weierstrass Theorem. Pointwise and uniform convergence. Cauchy criterion for uniform convergence. The Arzelà–
Ascoli Theorem. Weierstrass M-test. |
|
