Course Archives Theoretical Statistics and Mathematics Unit | |||||||||||||||||||||||||||||||||||||||||||
Course: Analysis III Instructor: Jishnu Biswas Room: G26 Level: Undergraduate Time: Currently offered |
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Syllabus 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. Evaluation:
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Midterm
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