Course Archives Theoretical Statistics and Mathematics Unit

Course: Analysis III Level: Undergraduate Time: Currently not offered

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. Top of the page Past Exams

Midterm 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 20s.pdf Solution 09.pdf 17.pdf 18.pdf Semestral 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 20.pdf 21.pdf 22.pdf Solution 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 20.pdf 20s.pdf 22.pdf Top of the page

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