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Titlebook: Intermediate Real Analysis; Emanuel Fischer Textbook 1983 Springer-Verlag New York, Inc. 1983 Differentialrechnung.Fischer.Integralrechnun

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书目名称Intermediate Real Analysis
编辑Emanuel Fischer
视频video
丛书名称Undergraduate Texts in Mathematics
图书封面Titlebook: Intermediate Real Analysis;  Emanuel Fischer Textbook 1983 Springer-Verlag New York, Inc. 1983 Differentialrechnung.Fischer.Integralrechnun
描述There are a great deal of books on introductory analysis in print today, many written by mathematicians of the first rank. The publication of another such book therefore warrants a defense. I have taught analysis for many years and have used a variety of texts during this time. These books were of excellent quality mathematically but did not satisfy the needs of the students I was teaching. They were written for mathematicians but not for those who were first aspiring to attain that status. The desire to fill this gap gave rise to the writing of this book. This book is intended to serve as a text for an introductory course in analysis. Its readers will most likely be mathematics, science, or engineering majors undertaking the last quarter of their undergraduate education. The aim of a first course in analysis is to provide the student with a sound foundation for analysis, to familiarize him with the kind of careful thinking used in advanced mathematics, and to provide him with tools for further work in it. The typical student we are dealing with has completed a three-semester calculus course and possibly an introductory course in differential equations. He may even have been expose
出版日期Textbook 1983
关键词Differentialrechnung; Fischer; Integralrechnung; calculus; real analysis
版次1
doihttps://doi.org/10.1007/978-1-4613-9481-5
isbn_softcover978-1-4613-9483-9
isbn_ebook978-1-4613-9481-5Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer-Verlag New York, Inc. 1983
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Functions,s the unordered pair consisting of . and .. By the .* (.,.) of elements . and ., we mean the set {.,.} together with the ordering of its members in which . is first and . second. We call . the . or . of (., .) and . its ..
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More on Series: Sequences and Series of Functions, exp and the trigonometric functions were derived in Chapter IV to use them in examples and problems illustrating the theorems on infinite series gathered there. As for the natural logarithm, this function was first defined in a later chapter, so we did not consider its series in Chapter IV. In this
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Preliminaries,We think of a . as a collection of objects viewed as a single entity. This description should not be regarded as a definition of a set since in it “set” is given in terms of “collection” and the latter is, in turn, in need of definition. Let us rather consider the opening sentence merely as a guide for our intuition about sets.
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Real Sequences and Their Limits,The subset relation ⊆ between sets has the following properties:
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