Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences (Encyclopedia of Mathematics and its Applications, Vol. 31) 1st Edition by J. Aczel (PDF)

Description

Deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioral, and social sciences. The authors emphasize applications, although not at the expense of theory, and have kept the prerequisites to a minimum; the reader should be familiar with calculus and some simple structures of algebra and have a basic knowledge of Lebesque integration. For the applications the authors have included references and explained the results used. The book is designed so that the chapters may be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. Each chapter concludes with exercises and further results, 400 in all, which extend and test the material presented in the text. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography of over 1600 items. This volume will be of interest to professionals and graduate students in pure and applied mathematics.

User’s Reviews

Editorial Reviews: Review “The book has been designed so that the chapters can be read almost independently of each other. This beautifully written treatise is very useful as a reference book for research workers in the area.” Mathematical Reviews”…this is an excellent reference book, in general, for senior and higher level physics students, and perhaps for numerical analysts working on computer algorithms….I would not hesitate to recommend this book to any physics and geophysics graduate students, as well as to some interested faculty members.” Physics in Canada Book Description This treatise deals with modern theory of functional equations in several variables and their applications to mathematics.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you have read Aczel’s book

⭐, then this is a natural continuation and I do not probably have to explain why you should read it.However, if you are not familiar with Janos Aczel, he is one of the authorities on functional equations. As is the case with the previous book too, the included material is great and carefully written, the presentation of the topics is clear and pedagogical, a big number of references are given and the publisher has done a superb job with the typesetting (I own a 1989 hardcover edition). Moreover, in this book, the authors have added end-of-the-chapter problems which are missing in Aczel’s previous book. Some selected problems are labelled with an asterisk to indicate an increased difficulty but, in some cases, I have found that these problems are not necessarily harder than other problems not labelled with an asterisk.Overall, it is a superb book and you should really read it if you have an interest in the topic. However, it is definitely written at a higher level than Aczel’s previous book. Therefore, if you have not read the previous book and/or you are not familiar with the subject, then you may want to start with that book first and then continue with this book.

⭐This and its precursor volume on functional equations by Aczel are the world’s greatest books on functioal equations in my opinion. Functional equations are among the most general equations in mathematics, and therefore anybody who wants to use equations however remote from physical sciences should buy and read these books (with the help of a consultant and/or tutor if necessary to explain them in approximately ordinary English). To give the reader an example, logarithms obey log(a times b) = log a + log b. It turns out that the form of this equation, f(a times b) = f(a) + f(b), characterizes logarithms uniquely under certain fairly general conditions. Functional equations like the last one turn out to uniquely characterize whole fields and categories of both commonly and uncommonly used equations ranging from probability and statistics to information theory and entropy and beyond. For example, how many people know that the bell-shaped curve (called the normal or Gaussian distribution) used in grading students on a curve or average has its own functional equation? Or how many people know that computer or cryptographic codes cannot be shorter than Shannon entropy for average codeword length because of its functional equation properties? Aczel and Dhombres cover these and many other topics. The book is published by Cambridge University Press, which is one of the world’s best publishing companies, and Aczel is at Waterloo University in Canada, while Dhombres is (at least, until recently) at a French university. Waterloo and most French universities are among the best in the world.

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Free Download Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences (Encyclopedia of Mathematics and its Applications, Vol. 31) 1st Edition in PDF format
Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences (Encyclopedia of Mathematics and its Applications, Vol. 31) 1st Edition PDF Free Download
Download Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences (Encyclopedia of Mathematics and its Applications, Vol. 31) 1st Edition 1989 PDF Free
Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences (Encyclopedia of Mathematics and its Applications, Vol. 31) 1st Edition 1989 PDF Free Download
Download Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences (Encyclopedia of Mathematics and its Applications, Vol. 31) 1st Edition PDF
Free Download Ebook Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences (Encyclopedia of Mathematics and its Applications, Vol. 31) 1st Edition