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