Course Archives    Theoretical Statistics and Mathematics Unit
Course: Analysis II
Level: Undergraduate
Time: Currently not offered
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.

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Past Exams
Midterm
04.pdf 05.pdf 06.pdf 07.pdf 08.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf
Solutions
15.pdf
Semestral
01.pdf 03.pdf 05.pdf 06.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf
Supplementary and Back Paper
04.pdf 06.pdf 10.pdf 11.pdf 12.pdf 15.pdf 16.pdf

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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]