Course Code and Name: MAT5101- Real Analysis
(September-January, 2023-24)
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Classes: Tue, 11:15-12:45 pm, Tutorial: 1:45-2:45 pm; Thu, 9:30-11am
Syllabus:
Real number system and its order completeness. Sequences and series of real numbers. Metric spaces: Basic concepts, continuous functions, Intermediate Value Theorem, Compactness, Heine-Borel Theorem.
Differentiation, Taylor's theorem, Riemann Integral, Improper integrals, Sequences and series of functions, Uniform convergence, power series, Fourier series, Weierstrass approximation theorem, equicontinuity, Arzela-Ascoli theorem.
Textbooks:
1. W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976.
2. Robert Gardner Bartle and Donald R. Sherbert, Introduction to Real Analysis, 4th Edition,Wiley, 2011.
References:
1. C.C. Pugh, Real Mathematical Analysis, Springer, 2002.
2. T. M. Apostol, Mathematical Analysis, 2nd Edition, Narosa, 2002.
3. G. F. Simmons, Introduction to Topology and Modern Analysis, McGraw-Hill, 1963.
4. Stephen Abbot, Understanding Analysis, Springer, New York, NY, 2015.
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