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Columbia Campus    
2017-2018 Graduate Studies Bulletin (Archived Copy) 
    
 
  Jun 29, 2022
 
2017-2018 Graduate Studies Bulletin (Archived Copy) [Archived Catalog]

MATH 703 - Analysis I

Credits: 3

Compactness, completeness, continuous functions. Outer measures, measurable sets, extension theorem and Lebesgue-Stieltjes measure. Integration and convergence theorems. Product measures and Fubini’s theorem. Differentiation theory. Theorems of Egorov and Lusin. Lp-spaces. Analytic functions: Cauchy-Riemann equations, elementary special functions. Conformal mappings. Cauchy’s integral theorem and formula. Classification of singularities, Laurent series, the Argument Principle. Residue theorem, evaluation of integrals and series.