Course  Code and Name: MAT5101- Real Analysis

(July-December, 2024-25)

       Classes: Tue, 11:15-12:45 pm, Tutorial: 1:45-2:45 pm; Thu, 9:30-11am
          Class Room-1, Department of Mathematics, Gangotri Block

Instructor: Manikandan Rangaswamy

Teaching Assistant: Santo Sali

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.