Sprache: Englisch
Verlag: World Scientific Publishing Co P, 2015
ISBN 10: 9814689084 ISBN 13: 9789814689083
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Sprache: Englisch
Verlag: Springer Nature Switzerland AG, 2021
ISBN 10: 3030827410 ISBN 13: 9783030827410
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Sprache: Englisch
Verlag: World Scientific Publishing Co Pte Ltd, SG, 2015
ISBN 10: 9814689092 ISBN 13: 9789814689090
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In den WarenkorbPaperback. Zustand: New. Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis.Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions.Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers.Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions.
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Sprache: Englisch
Verlag: Springer Nature Switzerland AG, CH, 2021
ISBN 10: 3030827410 ISBN 13: 9783030827410
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Sprache: Englisch
Verlag: Springer Nature Switzerland AG, Cham, 2021
ISBN 10: 3030827410 ISBN 13: 9783030827410
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Paperback. Zustand: new. Paperback. Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to singlevariable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof. Each chapter contains numerous examples and a large selection of exercises, as well as a Notes and Comments section, which highlights distinctive features of the exposition and provides additional references to relevant literature.This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises. A new chapter discusses sequences and series of realvalued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter. Two new appendices cover a construction of the real numbers using Cauchy sequences, and a selfcontained proof of the Fundamental Theorem of Algebra.In addition to the usual prerequisites for a first course in singlevariable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs. This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis. The authors A Course in Multivariable Calculus is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting.From reviews:[The first edition is] a rigorous, well-presented and original introduction to the core of undergraduate mathematics first-year calculus. It develops this subject carefully from a foundation of high-school algebra, with interesting improvements and insights rarely found in other books. [] This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously. N.J. Wildberger, Aust. Math. Soc. Gaz. Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to singlevariable calculus. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
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Sprache: Englisch
Verlag: World Scientific Publishing Co Pte Ltd, 2015
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Verlag: World Scientific Publishing Company, 2015
ISBN 10: 9814689084 ISBN 13: 9789814689083
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Sprache: Englisch
Verlag: World Scientific Publishing Company, 2015
ISBN 10: 9814689084 ISBN 13: 9789814689083
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Sprache: Englisch
Verlag: World Scientific Publishing Co Pte Ltd, Singapore, 2015
ISBN 10: 9814689092 ISBN 13: 9789814689090
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Paperback. Zustand: new. Paperback. Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis.Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions.Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers. Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions." Volume 1 covers the content of two typical modules in undergraduate course for mathematics: Part 1: Introductory calculus Part 2: Analysis of functions of one variable Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
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