Transcription of Mathematical Analysis, Second Edition
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Mathematical Analysis, Second Edition
PREFACEA glance at the table of contents will reveal that this textbooktreats topics inanalysis at the "Advanced Calculus" level. The aim has beento provide a develop-ment of the subject which is honest, rigorous, up to date, and, at thesame time,not too book provides a transition from elementary calculustoadvanced courses in real and complex function theory, and it introducesthe readerto some of the abstract thinking that pervades modern Second Edition differs from the first inmany respects. Point set topologyis developed in the setting of general metricspaces as well as in Euclidean n-space,and two new chapters have been addedon Lebesgue integration. The material online integrals, vector analysis , and surface integrals has beendeleted.
1.13 Properties of the integers deduced from the completeness axiom.. 10 1.14 The Archimedean property of the real-number system . . . . . 10 1.15 Rational numbers with finite decimal representation . . . . . 11
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