| Code |
Course Name |
Language |
Type |
| MAT 272E |
Advanced Mathematics |
English |
Compulsory |
| Local Credits |
ECTS |
Theoretical |
Tutorial |
Laboratory |
| 3 |
5 |
3 |
0 |
0 |
| Course Prerequisites and Class Restriction |
| Prerequisites |
MAT 188 MIN DD
or MAT 188E MIN DD
or MAT 213 MIN DD
or MAT 213E MIN DD
or MAT 104 MIN DD
or MAT 104E MIN DD
or MAT 102 MIN DD
or MAT 102E MIN DD
or MAT 186 MIN DD
or MAT 186E MIN DD
|
| Class Restriction |
None |
| Course Description |
| Sequences and series of real numbers and convergence. 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. Total Derivative. C^k[a,b] and
L^p spaces. Sequences and series of real valued functions on metric spaces. Pointwise and uniform convergence. Cauchy
criterion for uniform convergence. Weierstrass M-test. The Stone-Weierstrass Theorem. Hilbert spaces. |
|
