MA5330 Real Analysis

 

Course contents:

 

Real number system and its order completeness, sequences and series of real numbers.

 

Metric spaces: Basic concepts, continuous functions, completeness, Baire Category Theorem, Contraction mapping theorem, connectedness, Intermediate Value Theorem, Compactness, Heine-Borel Theorem.

 

Differentiation, Taylor's theorem, Riemann-Stieltjes integral and its properties, Improper integrals.

 

Sequences and series of functions, Uniform convergence, power series and Fourier series, Weierstrass approximation theorem, Equicontinuity, Arzela-Ascoli theorem.

 

Text Books:

 

1.      W. Rudin, Principles of Mathematical Analysis, Mc-Graw Hill, 1976.

2.      C. C. Pugh, Real Mathematical Analysis, Springer, 2002.

 

Reference:

 

  1. T. M. Apostol, Mathematical Analysis, Addison-Wesley, 1974.

2.      G. F. Simmons, Topology and Modern Analysis, Kreiger, 2003.