Course Archives Theoretical Statistics and Mathematics Unit
Course: Analysis III
Instructor: B Rajeev
Room: G26
Level: Undergraduate
Time: Currently offered
Past Exams

Syllabus (Vector Calculus): Multiple integrals, Existence of the Riemann integral for sufficiently well-behaved functions on rectangles, i.e. product of intervals. Multiple integrals expressed as iterated simple integrals. Brief treatment of multiple integrals on more general domains. Change of variables and the Jacobian formula, illustrated with plenty of examples. Inverse and implicit functions theorems (without proofs). More advanced topics in the calculus of one and several variables curves in R2 and R3 . Line integrals, Surfaces in R3, Surface integrals, Divergence, Gradient and Curl operations, Green's, Strokes' and Gauss' (Divergence) theorems. Sequence of functions - pointwise versus uniform convergence for a function defined on an interval of R, integration of a limit of a sequence of functions. The Weierstrass's theorem about uniform approximation of a continuous function by a sequence of polynomials on a closed bounded interval.

Midterm Exam 40 marks
Assignment -- marks
Final Exam 60 marks
Total 100 marks

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Past Exams
05.pdf 06.pdf 08.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf 20.pdf
09.pdf 17.pdf 18.pdf
02.pdf 05.pdf 07.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf
09.pdf 17.pdf 18.pdf
Supplementary and Back Paper
06.pdf 07.pdf 10.pdf 11.pdf 12.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf

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[ Semester Schedule ][ SMU ] [Indian Statistical Institute]