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Titlebook: Real Mathematical Analysis; Charles Chapman Pugh Textbook 20021st edition Springer Science+Business Media New York 2002 Real Mathematical

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書目名稱Real Mathematical Analysis
編輯Charles Chapman Pugh
視頻videohttp://file.papertrans.cn/823/822179/822179.mp4
概述The exposition is informal and relaxed, with many helpful asides, and examples.Contains an excellent selection of more than 500 exercises.Ideal for self-study
叢書名稱Undergraduate Texts in Mathematics
圖書封面Titlebook: Real Mathematical Analysis;  Charles Chapman Pugh Textbook 20021st edition Springer Science+Business Media New York 2002 Real Mathematical
描述Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE‘s . . . . . . . . 228 5
出版日期Textbook 20021st edition
關(guān)鍵詞Real Mathematical Analysis; calculus; integral; mathematical analysis; real analysis; real number
版次1
doihttps://doi.org/10.1007/978-0-387-21684-3
isbn_softcover978-1-4419-2941-9
isbn_ebook978-0-387-21684-3Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer Science+Business Media New York 2002
The information of publication is updating

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Functions of a Real Variable,the change in the independent variable ., while Δ. (.) — f (.) is the resulting change in the dependent variable . (.). Differentiability at . means that . We begin by reviewing the proofs of some standard calculus facts.
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Function Spaces,unction? What should it mean that they get closer and closer to a limit function? The simplest idea is that a sequence of functions .. converges to a limit function . if for each ., the values ..(.) converge to . (.) as . → ∞. This is called pointwise convergence: a sequence of functions .. : [.] →
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0172-6056 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE‘s . . . . . . . . 228 5 978-1-4419-2941-9978-0-387-21684-3Series ISSN 0172-6056 Series E-ISSN 2197-5604
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