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Taylor (mathematics, U. of Utah) has developed a textbook from notes for a two-semester undergraduate course he teaches for students who have completed three semesters of calculus and one semester of linear algebra. For many students, he says, this is the first course in which everything is proved rigorously, and they are expected to create proofs as well as understand them. He presents a rigorous development of the calculus, beginning with a study of the properties of the real number system. The topics include sequences, the derivation, infinite series, convergence in Euclidean space, differential in several variables, and vector calculus. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)
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Über die Autorin bzw. den Autor
Joseph L. Taylor, University of Utah, Salt Lake City, UT, USA
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Foundations of Analysis (Pure and Applied Undergraduate Texts: Sally, 18)
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American Mathematical Society (edition ), 2012
ISBN 10: 0821889842
ISBN 13: 9780821889848
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Foundations of Analysis
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American Mathematical Society, 2012
ISBN 10: 0821889842
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Hardback. Zustand: Good. Analysis plays a crucial role in the undergraduate curriculum. Building upon the familiar notions of calculus, analysis introduces the depth and rigor characteristic of higher mathematics courses. Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. The list of topics covered is rather standard, although the treatment of some of them is not. The several variable material makes full use of the power of linear algebra, particularly in the treatment of the differential of a function as the best affine approximation to the function at a given point. The text includes a review of several linear algebra topics in preparation for this material. In the final chapter, vector calculus is presented from a modern point of view, using differential forms to give a unified treatment of the major theorems relating derivatives and integrals: Green's, Gauss's, and Stokes's Theorems. At appropriate points, abstract metric spaces, topological spaces, inner product spaces, and normed linear spaces are introduced, but only as asides. That is, the course is grounded in the concrete world of Euclidean space, but the students are made aware that there are more exotic worlds in which the concepts they are learning may be studied. Artikel-Nr. 00098532332
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Foundations of Analysis
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American Mathematical Society, 2012
ISBN 10: 0821889842
ISBN 13: 9780821889848
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Hardback. Zustand: Very Good. Analysis plays a crucial role in the undergraduate curriculum. Building upon the familiar notions of calculus, analysis introduces the depth and rigor characteristic of higher mathematics courses. Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. The list of topics covered is rather standard, although the treatment of some of them is not. The several variable material makes full use of the power of linear algebra, particularly in the treatment of the differential of a function as the best affine approximation to the function at a given point. The text includes a review of several linear algebra topics in preparation for this material. In the final chapter, vector calculus is presented from a modern point of view, using differential forms to give a unified treatment of the major theorems relating derivatives and integrals: Green's, Gauss's, and Stokes's Theorems. At appropriate points, abstract metric spaces, topological spaces, inner product spaces, and normed linear spaces are introduced, but only as asides. That is, the course is grounded in the concrete world of Euclidean space, but the students are made aware that there are more exotic worlds in which the concepts they are learning may be studied. Artikel-Nr. 00107978273
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Foundations of Analysis
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Foundations of Analysis (Pure and Applied Undergraduate Texts)
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American Mathematical Society, 2012
ISBN 10: 0821889842
ISBN 13: 9780821889848
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Foundations of Analysis
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Taylor, J: Foundations of Analysis
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Zustand: New. KlappentextrnrnFoundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous de. Artikel-Nr. 595068220
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Foundations of Analysis (Pure and Applied Undergraduate Texts: Sally, 18)
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Foundations of Analysis
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ISBN 10: 0821889842
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Buch. Zustand: Neu. Neuware - Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. Artikel-Nr. 9780821889848
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