MA 224

REAL ANALYSIS

3-0-0-6

Prerequistes: Nil

Syllabus:

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.

Textbooks:

1.   J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, 2nd Ed., W. H. Freeman, 1993.

2.   M. Capinski and E. Kopp, Measure, Integral and Probability, 2nd Ed., Springer, 2007.

References:

1.   N. L. Carothers, Real Analysis, Cambridge University Press, 2000.

2.   G. de Barra, Measure Theory and Integration, New Age International, 1981.

3.   R. C. Buck, Advanced Calculus, Waveland Press Incorporated, 2003.