Functional Equations And How To Solve Them

Author : Christopher G. Small
Publisher : Springer Science & Business Media
Page : 139 pages
File Size : 46,9 Mb
Release : 2007-04-03
Category : Mathematics
ISBN : 9780387489018

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Functional Equations and How to Solve Them by Christopher G. Small Pdf

Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.

Author : Costas Efthimiou
Publisher : American Mathematical Soc.
Page : 381 pages
File Size : 51,7 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9780821853146

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Introduction to Functional Equations by Costas Efthimiou Pdf

Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Author : J. Smital
Publisher : CRC Press
Page : 164 pages
File Size : 49,8 Mb
Release : 2020-08-26
Category : Mathematics
ISBN : 9781000112184

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On Functions and Functional Equations by J. Smital Pdf

On Functions and Functional Equations introduces the main topics in iteration theory and the theory of functional equations with emphasis on applications in the fields of mathematics, physics, biology, chemistry, and electronics and mechanical engineering. The book contains many classical results as well as important, more recent results. It also includes numerous exercise and some problems that have yet to be resolved. The book is accessible to readers having a secondary level mathematical education.

Author : Henrik Stetkaer
Publisher : World Scientific
Page : 396 pages
File Size : 43,9 Mb
Release : 2013-07-15
Category : Mathematics
ISBN : 9789814513142

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Functional Equations On Groups by Henrik Stetkaer Pdf

This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, ℝ). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.

Author : Sui Sun Cheng,Wenrong Li
Publisher : World Scientific
Page : 296 pages
File Size : 52,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812793348

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Analytic Solutions of Functional Equations by Sui Sun Cheng,Wenrong Li Pdf

This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.

Author : Enrique Castillo,Andres Iglesias,Reyes Ruiz-Cobo
Publisher : Elsevier
Page : 410 pages
File Size : 43,8 Mb
Release : 2004-11-04
Category : Mathematics
ISBN : 9780080477916

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Functional Equations in Applied Sciences by Enrique Castillo,Andres Iglesias,Reyes Ruiz-Cobo Pdf

The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved. A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems. An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm. The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications. · A general methodology for solving functional equations is provided in Chapter 2. · It deals with functional networks, a powerful generalization of neural networks. · Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, illustrate the concept of functional equation. · Functional equations are presented as a powerful alternative to differential equations. · The book contains end of chapter exercises.

Author : J. Aczel,Hansjorg Oser
Publisher : Courier Corporation
Page : 548 pages
File Size : 46,6 Mb
Release : 2006-02-01
Category : Mathematics
ISBN : 9780486445236

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Lectures on Functional Equations and Their Applications by J. Aczel,Hansjorg Oser Pdf

Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.

Author : Stefan Czerwik
Publisher : World Scientific
Page : 424 pages
File Size : 44,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9810248377

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Functional Equations and Inequalities in Several Variables by Stefan Czerwik Pdf

This book outlines the modern theory of functional equations and inequalities in several variables. It consists of three parts. The first is devoted to additive and convex functions defined on linear spaces with semilinear topologies. In the second part, the problems of stability of functional equations in the sense of Ulam-Hyers-Rassias and in some function spaces are considered. In the last part, the functional equations in set-valued functions are dealt with ? for the first time in the mathematical literature. The book contains many fresh results concerning those problems.

Author : Amir Hossein Parvardi
Publisher : Unknown
Page : 171 pages
File Size : 49,6 Mb
Release : 2018-05-29
Category : Electronic
ISBN : 1983024465

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Functional Equations in Mathematical Olympiads (2017 - 2018) by Amir Hossein Parvardi Pdf

Functional equations, which are a branch of algebraic problems used in mathematical competitions, appear in recent olympiads very frequently. The current book is the first volume in a series of books on collections of solved problems in functional equations. This volume contains 175 problems on the subject, including those used in latest mathematical olympiads (2017 - 2018) around the world. The basic concepts of functional equations and techniques of problem solving have been briefly discussed in the preamble of the book.

Author : Prasanna K. Sahoo,Palaniappan Kannappan
Publisher : CRC Press
Page : 465 pages
File Size : 50,9 Mb
Release : 2011-02-08
Category : Mathematics
ISBN : 9781439841167

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Introduction to Functional Equations by Prasanna K. Sahoo,Palaniappan Kannappan Pdf

Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as p

Author : John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar
Publisher : World Scientific Publishing Company
Page : 396 pages
File Size : 44,7 Mb
Release : 2017-03-20
Category : Electronic
ISBN : 9789813147621

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Functional Equations and Inequalities by John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar Pdf

This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations. Request Inspection Copy

Author : Enrique Castillo
Publisher : CRC Press
Page : 354 pages
File Size : 46,8 Mb
Release : 1992-05-27
Category : Mathematics
ISBN : 082478717X

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Functional Equations and Modelling in Science and Engineering by Enrique Castillo Pdf

Provides engineers and applied scientists with some selected results of functional equations and their applications, with the intention of changing the way they think about mathematical modelling. Many of the proofs are simplified or omitted, so as not to bore or confuse engineers. Functional equati

Author : Paulo Ney de Souza,Jorge-Nuno Silva
Publisher : Springer Science & Business Media
Page : 614 pages
File Size : 48,7 Mb
Release : 2004-01-08
Category : Mathematics
ISBN : 0387204296

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Berkeley Problems in Mathematics by Paulo Ney de Souza,Jorge-Nuno Silva Pdf

This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.

Author : Marek Kuczma
Publisher : Unknown
Page : 394 pages
File Size : 54,5 Mb
Release : 1968
Category : Mathematics
ISBN : WISC:89041213521

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Functional Equations in a Single Variable by Marek Kuczma Pdf

Author : J. Aczel
Publisher : Springer
Page : 72 pages
File Size : 48,6 Mb
Release : 1969
Category : Juvenile Nonfiction
ISBN : UOM:39015017336119

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On Applications and Theory of Functional Equations by J. Aczel Pdf