Mathematical AnalysisA text for an advanced-undergraduate/graduate course in real analysis. This revised edition (1st was in 1985) adds a chapter on metric spaces discussing completeness, compactness, and connectedness of the spaces, and two appendices discussing Beta-Gamma functions and Cantor's theory of real numbers. Annotation copyright by Book News, Inc., Portland, OR |
Contents
Real Numbers | 1 |
Open and Closed Sets | 25 |
Real Sequences | 42 |
Copyright | |
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a₁ absolutely convergent b₁ bounded and integrable bounded function bounded variation Cauchy sequence Cauchy's closed interval converges uniformly cos² curve defined definition denoted differentiable diverges domain double integral dx converges dx dy dz dz dx equal equation Evaluate Example exists f dx f is continuous f is integrable finite number function f ƒ dx dy ƒ dy ƒ is bounded Hence improper integral infimum Lebesgue integrable lim f(x limit point line integral m₁ Mean Value Theorem monotonic increasing neighbourhood nx dx partial derivatives partial sums partition positive integer positive number power series prove rational number real numbers S₁ series converges Show Similarly subset supremum surface integral Test Un+1 uniformly convergent upper bound xy-plane zero ди ду дх