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

Syllabus: The existence of Riemann integral for sufficiently well behaved functions. Fundamental theorem of Calculus, computation of definite integrals, improper integrals, sequences and series of functions, double sequences, pointwise versus uniform convergence for a function defined on an interval of R, term by term differentiation and integration, the Weierstrasss theorem about uniform approximation of a continuous function by a sequence of polynomials on a closed bounded interval. Radius of convergence of power series and real analyticity of functions.

Reference Texts:

(a) T. M. Apostol: Mathematical Analysis.
(b) T. M. Apostol: Calculus.
(c) S. Dineen: Multivariate Calculus and Geometry.
(d) R. R. Goldberg: Methods of Real Analysis.
(e) T. Tao: Analysis I & II.
(f) Bartle and Sherbert: Introduction to Real Analysis.
(g) H. Royden: Real Analysis.
(h) K. A. Ross: Elementary Analysis.

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Past Exams
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