Course Archives Theoretical Statistics and Mathematics Unit | ||||||||||||||||||||||||||||||||||||||||||||||||
Course: Analysis II Instructor: Jaydeb Sarkar Room: G24 Level: Undergraduate Time: Currently offered |
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Syllabus Past Exams Syllabus (Metric spaces and Multivariate Calculus): The existence of Riemann integral for sufficiently well behaved functions. Fundamental theorem of Calculus. Calculus of several variables: Differentiability of maps from R^m to R^n and the derivative as a linear map. Higher derivatives, Chain Rule, Taylor expansions in several variables, Local maxima and minima, Lagrange multiplier.Elements of metric space theory - sequences and Cauchy sequences and the notion of completeness, elementary topological notions for metric spaces i.e.open sets, closed sets, compact sets, connectedness, continuous and uniformly continuous functions on a metric space. The Bolzano - Weirstrass theorem, Supremum and infimum on compact sets, R^n as a metric space. Evaluation:
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Midterm
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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute] |