Real Analysis

Code: MA2221 | L-T-P-C: 3-0-0-6

Metrics and norms: metric spaces, normed vector spaces, convergence in metric spaces, completeness, compactness; Functions of several variables: differentiability, chain rule, Taylor's theorem, inverse function theorem, implicit function theorem; Lebesgue measure and integral: sigma-algebra of sets, measure space, Lebesgue measure, measurable functions, Lebesgue integral, Fatou’s lemma, dominated convergence theorem, monotone convergence theorem L^P  spaces.

Texts:

• J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, Second Edition, W. H. Freeman, 1993.
• M. Capinski and E. Kopp, Measure, Integral and Probability, Second Edition, Springer, 2004.

 

References:

• N. L. Carothers, Real Analysis, Cambridge University Press, 2000.
• G. de Barra, Measure Theory and Integration, New Age International, 1981
• R. C. Buck, Advanced Calculus, Third Edition, Waveland Press Incorporated, 2004.