Product Description
This new single-volume edition combines two parts of a renowned mathematician’s collection of instructive problems. Vol. I contains more than 300 elementary problems dealing with fundamental concepts, infinite sequences and series, functions of a complex variable, conformal mapping, and more. Vol. II features over 230 problems in advanced theory—singularities, entire and meromorphic functions, periodic functions, analytic continuation, multiple-valued functions and Riemann surfaces, and more. Solution hints are provided, plus complete solutions to all problems.
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Product Description
Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler’s summation formula, asymptotic expansions, other topics). Exercises throughout. Ideal for self-study.
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Customer Reviews (4)

How to tell if you are a "formalist" --
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!

This is an ok book
To be honest alot of the work does not make immediate sense. Knopp leaves alot of important details out in his proofs and sometimes tends to rite to informal a proof of theorems. Theres no answers to the questions and i found that i became bored while reading the book. There are better. I have a large collection of books and the infinite series sections or chapters in them are better than alot of this book. I think that its main problem is that it cannot be easily accessible to beginners although it claims this. well apart from the begin chapters.

A Truly Marvelous Value
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 fullof recipes and explanations of many of those little annoying points youdon't understand fully.Do you REALLY understand what 'asymptoticallyequal to (~)' means? Heartily recommended!

The best book on infinite series
Excellent book for consulting with lots of examples and problems. Verywell written but with the problem of very old notation. Everything you needto know about series is in this book. Very good to use in problems seminars ... Read more

Product 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, tests for infinite series, power series, numerical and closed evaluation of series.
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Customer Reviews (3)

Not suitable for people who want to learn from scratch
Learning infinite sequences from this book is not recommended for beginners like me. I suggest reading Calculus by John Stewart where evaluation of limits is demonstrated. Stewart proceeds along with different types of tests compared to this book.

This one is more "formula oriented"

Regards,
Yasir
[...]

A good presentation of a not so easy subject
Do a series of numbers converge or diverge? That is, does the series you are looking at go on forever, or end in some number? How do sequences and sets relate to each other? Is there a set that contains infinite sequences? From the expansion of elementary functions, to the power series, this book makes your journey into this area of mathematics understandable, even enjoyable. If you are a MathPhile, or want to be, this book is highly recommended.

Nice book on infinite sequences and series.
Very dry, hard to read for long periods.The 174 pages seem like about 300. I think this could be due to the translation.Very complete, gives you everything you could want to know about infinite series.*Not* forthose of you who are easily bored... ... Read more

Product Description
Two volumes of a classic five-volume work in one handy edition. Part I considers general foundations of the theory of functions; Part II stresses special functions and characteristic, important types of functions, selected from single-valued and multiple-valued classes. Demonstrations are full and proofs given in detail. Introduction. Bibliographies.
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Customer Reviews (2)

Truly a gem of a book.
This elegant little book covers the elements of a senior or 1st year graduate course on complex analysis, although a really good mathematics program like at Berkeley may look upon it as providing some material for a junior course in advanced calculus. It is not a new book, i.e. it predates the space age and computers, but the material is timeless and fundamental. Highly recommended for those who want some exposure to a first-class style in mathematics.

a short review of the book theory of functions by Knopp
Despite not being a very recent book, a graduate student of mathematics who has to prepare complex analysis as a general topic for his qualifying examinations may find that this text covers all the essential material inthe subject. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.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. ... Read more

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Customer Reviews (3)

Very Clear and Sharp Mentor of Math +++
Recently, I dug into my collection of "old-school" math books looking for a good review of general function theory via complex variables. I [somehow] recalled this author as having a very good approach to this area. This topic is so wide and deep as to allow for many approaches. The whole presentation of this author via his little series of math works follows a very clear and sharp path from complex variables to general function theory. It seems many authors delay starting at the start with complex numbers and variables -- yet the "complex way" is a very streamlined way into general function theory and even infinite series -- as this Mentor shows -- starting with this very great little gem of an introduction. Even complex numbers can be approached from various angles -- one of the best being that of "Elements of the Theory of Functions" by Konrad Knopp +++

A Classic with outdated language
This book goes with the series of books written by this author:" Theory of Functions". Together with the other parts it gives a good introduction to the theory of complex functional analysis.Although the language is in places outdated, the mathematics covered is solid and necessary. It is a starting point in study for subjects like chaos and fractals as well. One of the best points is that is a cheap Dover book!

A Gem!
This book would be worth the price of it were 10 times as expensive!One of the best presentations of the real and complex analysis I have seen. ... Read more

Product Description
Der Erwerb des Buches enthält gleichzeitig die kostenlose Mitgliedschaft im Buchklub des Verlags zum Ausprobieren - dort können Sie von über einer Million Bücher ohne weitere Kosten auswählen. Das Buch besteht aus Wikipedia-Artikeln: Guido Knopp, Konrad Löw, Wolfgang Stock, Leo Scheffczyk, Lothar Roos, Michael Dieterich, Heinrich Beck, Leo Elders, Anton Ziegenaus, Peter Beyerhaus, Ernst Haag, Karel Mácha, Hartmut Fröschle, Werner Münch, Johannes Stöhr, Wolfgang Waldstein, Theobald Beer, Helmut Moll, Manfred Lochbrunner, Ulrich Hoyer, Joachim Piegsa, Alma von Stockhausen, Reinhold Ortner, Miloš Lokajícek, Remigius Bäumer, Roland Süßmuth, Lutz Sperling,. Online finden Sie die kostenlose Aktualisierung der Bücher. Nicht dargestellt. Auszug: Guido Friedrich Knopp (* 29. Januar 1948 in Treysa, Hessen) ist ein deutscher Journalist, Publizist und Moderator. Er ist vor allem für seine Beschäftigung mit zeitgeschichtlichen Themen bekannt. Guido Knopps Familie stammt aus Oberschlesien. Nach der Vertreibung kamen sie nach Aschaffenburg, wo Guido Knopp aufwuchs. Nach seinem Abitur am Friedrich-Alexander-Gymnasium Neustadt an der Aisch studierte Knopp Geschichte, Politik und Publizistik in Frankfurt am Main, Amsterdam und Würzburg. Nach seiner Promotion über die Geschichte der SPD arbeitete er als Redakteur bei der Welt am Sonntag und der Frankfurter Allgemeinen Zeitung. Seit 1978 ist Knopp beim ZDF beschäftigt, wo er die ZDF-Redaktion „Zeitgeschichte" aufbaute, die seit den neunziger Jahren von Knopp moderierte zeitgeschichtliche Fernsehserien wie Hitler - Eine Bilanz, Unser Jahrhundert - Deutsche Schicksalstage, Hitlers Helfer, Hitlers Krieger und History produziert. Zu den Dokumentationen veröffentlichte Knopp auch mehrere Begleitbücher, die hohen Umsatz fanden. Seit 1999 wiederholt Phoenix die von Knopp damals für das ZDF anlässlich des Jahrtausendwechsels entwickelte und moderierte Reihe 100 Jahre, die die Geschichte des 20. Jahrhunde...http://booksllc.net/?l=de&id=413121 ... Read more