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Metric Topology II and complex analysis Description

Key Elements

Code

MATH 209

Formation

BS Mathematics

Semester

4

Credits

6

Number of Teaching Hours

30

Number of Tutoring Sessions

30

Number of Laboratory Sessions

0

Content

Objective

Content

I. Connected Metric Spaces: 1. Definition, connex subspaces of R, theorems and properties 2. Continuity et connexity, Intermediate value theorem, Product space. 3. Path-Connected Spaces : definitions et properties Hilbert Spaces: 1. Hermitian Form, Cauchy-Schwarz’ Inequqlity, Inner Product, préhilbert Spaces. 2. Orthogonality- theoreme of Pythagore, orthogonal projection. 3. Topological Dual of Hilbert Spaces, Representation Theorem of Riez. 4. Orthogonal Systems – Bessel’s Inequality, Parseval’s Inequality Riemman Integral: 1. Definition: Stairs Function and its Integral. 2. Integrable function in the sense of Riemann- properties et theorems. 3. Piecewise Continuity. 4. Indefinite Integral – Antiderivative. II. Complex Analysis: Continuity, differentiability, elementary functions, complex integrals, Cauchy’s formula, Power series, isolated singular points, Residue and Poles, Integration.