Convergent Series PDF Download

Author: Larry Niven
Publisher: Del Rey
ISBN: 9780345314109
Category :
Languages : en
Pages : 227

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Author: Daniel D. Bonar
Publisher: American Mathematical Soc.
ISBN: 1470447827
Category : Mathematics
Languages : en
Pages : 278

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Book Description
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.

Author: Charles Swartz
Publisher: World Scientific
ISBN: 9812833889
Category : Mathematics
Languages : en
Pages : 264

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Book Description
If ? is a space of scalar-valued sequences, then a series ?j xj in a topological vector space X is ?-multiplier convergent if the series ?j=18 tjxj converges in X for every {tj} e?. This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the OrliczOCoPettis theorem are derived for multiplier convergent series with respect to various locally convex topologies. Variants of the classical HahnOCoSchur theorem on the equivalence of weak and norm convergent series in ?1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.

Author: Charles Sheffield
Publisher: Baen
ISBN: 9780671877910
Category : Fiction
Languages : en
Pages : 580

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Convergent Series

Author: George R. McGhee
Publisher: MIT Press
ISBN: 0262016427
Category : Computers
Languages : en
Pages : 335

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Book Description
Convergent evolution occurs on all levels, from tiny organic molecules to entire ecosystems of species.

Author: Charles Napoleon Moore
Publisher: American Mathematical Soc.
ISBN: 0821846205
Category : Mathematics
Languages : en
Pages : 114

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Book Description
Fairly early in the development of the theory of summability of divergent series, the concept of convergence factors was recognized as of fundamental importance in the subject. One of the pioneers in this field was C. N. Moore, the author of the book under review.... Moore classifies convergence factors into two types. In type I he places the factors which have only the property that they preserve convergence for a convergent series or produce convergence for a summable series. In type II he places the factors which not only maintain or produce convergence but have the additional property that they may be used to obtain the sum or generalized sum of the series. This book gives a generalized systematic treatment of the theory of convergence factors of both types, for simply infinite series and for multiple series, convergent and summable.... --Bulletin of the American Mathematical Society

Author: Henry Parker Manning
Publisher:
ISBN:
Category : Irrational numbers
Languages : en
Pages : 164

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Author: Ted R Schultz
Publisher: MIT Press
ISBN: 0262543206
Category : Social Science
Languages : en
Pages : 339

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Contributors explore common elements in the evolutionary histories of both human and insect agriculture resulting from convergent evolution. During the past 12,000 years, agriculture originated in humans as many as twenty-three times, and during the past 65 million years, agriculture also originated in nonhuman animals at least twenty times and in insects at least fifteen times. It is much more likely that these independent origins represent similar solutions to the challenge of growing food than that they are due purely to chance. This volume seeks to identify common elements in the evolutionary histories of both human and insect agriculture that are the results of convergent evolution. The goal is to create a new, synthetic field that characterizes, quantifies, and empirically documents the evolutionary and ecological mechanisms that drive both human and nonhuman agriculture. The contributors report on the results of quantitative analyses comparing human and nonhuman agriculture; discuss evolutionary conflicts of interest between and among farmers and cultivars and how they interfere with efficiencies of agricultural symbiosis; describe in detail agriculture in termites, ambrosia beetles, and ants; and consider patterns of evolutionary convergence in different aspects of agriculture, comparing fungal parasites of ant agriculture with fungal parasites of human agriculture, analyzing the effects of agriculture on human anatomy, and tracing the similarities and differences between the evolution of agriculture in humans and in a single, relatively well-studied insect group, fungus-farming ants.

Author: Henry Burchard Fine
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 616

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Author: Konrad Knopp
Publisher: Courier Corporation
ISBN: 0486152049
Category : Mathematics
Languages : en
Pages : 212

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Book Description
Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.