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Theory And Application Of Infinite Series, by Konrad Knopp
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This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
- Sales Rank: #10502045 in Books
- Published on: 2011-09-12
- Original language: English
- Number of items: 1
- Dimensions: 9.69" h x 1.17" w x 7.44" l, 2.25 pounds
- Binding: Paperback
- 580 pages
Language Notes
Text: English
Original Language: German
Most helpful customer reviews
29 of 32 people found the following review helpful.
A Truly Marvelous Value
By Tony Aponick
The last chapter on the Euler-MacLauren summation formula, and attendant interrelations among the Zeta function, Bernoulli Numbers and Bernoulli Polynomials is alone worth three times the price of this gem. Chock full of recipes and explanations of many of those little annoying points you don't understand fully. Do you REALLY understand what 'asymptotically equal to (~)' means? Heartily recommended!
38 of 47 people found the following review helpful.
How to tell if you are a "formalist" --
By V. N. Dvornychenko
Anything to do with "infinity" is fascinating. Much of the history of mathematics has been a duel between those who see "infinity" as a delusion and impediment to progress, and those who see it as the greatest tool in the mathematician's toolbox. Infinite series, which may be loosely defined as sums of an infinite number of terms (numbers), take on some of this fascination. Although this book will appeal mainly to the professional mathematician, there is enough historical and elementary material to profit many college students- and possibly even some high school students.
Professional mathematician will find this book useful for filling in gaps left by topics not covered in traditional courses. An example is the detailed discussion of Euler's summation formula, which goes far beyond the simplified form usually encountered in textbooks. Another fascinating topic covered is divergent series, and methods by which meaningful sums can be assigned to these. There is something counterintuitive -- and, frankly, mind-boggling -- about many of these results.
Mathematicians can be put into several categories: 1) applied-mathematicians/computer-scientists/engineers concerned with solving practical problems, 2) those concerned with pedagogy and the history of mathematics, 3) epistemology and rigorous proofs, and 4) formalists. The fourth category, formalists, is difficult to define, but may be described as those that emphasize obtaining new results through formal (technical) manipulations, without undue concern regarding the meaning of the intermediate steps. The greatest exponents of this art were Euler and Ramanujan, though Fourier, Dirac and Heaviside are also solid members of this camp.
I take this digression because I feel that this book mainly appeals to the fourth type of mathematician. Although there are some general results in the theory of infinite series, any competent mathematicians can, in a few minutes, write a dozen infinite series which defy summation. As an example, the series associated with the Riemann zeta function of EVEN arguments were first summed by Euler. The sums arising from ODD arguments have defied summation to this day. Why this should be so is intriguing, but unknown. Incidentally, Euler's method of summation will make a "rigorists" hair stand upon ends. But he got the job done!
4 of 4 people found the following review helpful.
Kindle edition flawed
By John W. Scott
The Kindle edition is a flawed copy of the paper edition. I only have two examples, but being a math text where every symbol counts, that's enough for me to abandon the electronic version in favor of the paper version.
Example 1: Page 6 in the print book compares sets named M and N, but on the Kindle these are both referred to as M.
Example 2: Reference numbers set aside in the margin of the paper edition get interspersed throughout the Kindle edition. This is confusing as they sometimes come in the middle of an ordered list.
I encountered both problems very early, so there may be many more problems. The text is already a challenge for me, so I don't need additional, unnecessary problems to sort out. I do not recommend the Kindle version.
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