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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. The order ofsome chapters has been rearranged, many sections have been completely rewritten,and several new exercises have been development of Lebesgue integration follows the Riesz-Nagyapproachwhich focuses directly on functions and their integrals and doesnot depend onmeasure treatment here is simplified, spread out, and somewhatrearranged for presentation at the undergraduate first Edition has been used in mathematicscourses at a variety of levels,from first-year undergraduate to first-year graduate, bothas a text and as supple-mentary Second Edition preserves this example,Chapters 1 through 5, 12, and 13 providea course in differential calculus of func-tions of one or mor

is developed in the setting of general metric spaces as well as in Euclidean n-space, and two new chapters have been added on Lebesgue integration. The material on line integrals, vector analysis, and surface integrals has been deleted. The order of some chapters has been rearranged, many sections have been completely rewritten,

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