Real Analysis
Real Analysis
Mid Semester Examinations - 30% (15%+15%)
End Semester Examination - 30%
Quizzes - 30%
Assignments - 10%
Topics to be covered:
Real Number System, Limits and Continuity : Countable and uncountable sets, the axiom of choice, Zorn’s lemma, Real number system, Consequences of completeness property, limit and continuity of functions, uniform continuity.Metric Spaces : Metric spaces, continuous and uniformly continuous functions, bounded and totally bounded sets, Compactness, Heine-Borel Theorem, Completeness, Cantor’s Intersection theorem, Baire spaces, Connectedness. Sequences and Series of Functions: Sequences and Series of functions, Uniform convergence, Uniform convergence and integration, Uniform convergence and differentiation,Multivariable Calculus : Functions of several variables, continuity, differentiability, partial derivatives, Jacobian, Inverse Function Theorem and the Implicit Function Theorem, multivariable integration, Fubini’s theorem, Change of variables, Line integrals, surface integrals, Green’s theorem, Divergence theorem, Stokes theorem, and applications.References: