MA1L304
Undergraduate (ITEP)
· Generally offered: Spring
Real Analysis
L 3 T 1 P 0 Credits 4 Hours 4
Unit I: Real Number system, Supremum and Infimum, Archimedean property, Sequences and Series, Cauchy sequence and completeness, Convergence tests for series.
Unit II: Riemann Integral, Riemann Integrable functions, the fundamental theorems of calculus and their consequences, Improper Integrals.
Unit III: Sequence and series of functions, Uniform convergence and its relation with continuity, differentiability and integrability.
Unit IV: Metric spaces, Interior points and limit points, open, closed and perfect sets. Connected and compact sets, Bolzano-Weierstrass theorem.
Full syllabus document →
Unit II: Riemann Integral, Riemann Integrable functions, the fundamental theorems of calculus and their consequences, Improper Integrals.
Unit III: Sequence and series of functions, Uniform convergence and its relation with continuity, differentiability and integrability.
Unit IV: Metric spaces, Interior points and limit points, open, closed and perfect sets. Connected and compact sets, Bolzano-Weierstrass theorem.