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functional equations and how to solve them christopher small [pdf]

Functional Equations and How to Solve them by Christopher G. Small

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About this book :-
Functional Equations and How to Solve them written by Christopher Small
This books is best for the student who encounters a functional equation on a mathematics contest will need to investigate solutions to the equation by finding all solutions (if any) or by showing that all solutions have a particular property. Our emphasis is on the development of those tools which are most useful in giving a family of solutions to each functional equation in explicit form.

Book Detail :-
Title: Functional Equations and How to Solve them
Author(s): Christopher G. Small
Publisher: Springer
Year: 2007
Pages: 139
Type: PDF
Language: English
ISBN: 978-0-387-34539-0, 978-0-387-48901-8
Country: US
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Book Contents :-
Functional Equations and How to Solve them written by Christopher Small cover the following topics.
An historical introduction
Preliminary remarks, Nicole Oresme, Gregory of Saint-Vincent, Augustin-Louis Cauchy, What about calculus?, Jean d’Alembert, Charles Babbage, Mathematics competitions and recreational mathematics, A contribution from Ramanujan, Simultaneous functional equations, A clarification of terminology, Existence and uniqueness of solutions, Problems
Functional equations with two variables
Cauchy’s equation, Applications of Cauchy’s equation, Jensen’s equation, Linear functional equation, Cauchy’s exponential equation, Pexider’s equation, Vincze’s equation, Cauchy’s inequality, Equations involving functions of two variables, Euler’s equation, D’Alembert’s equation, Problems
Functional equations with one variable
Introduction, Linearization, Some basic families of equations, menagerie of conjugacy equations, Finding solutions for conjugacy equations, The Koenigs algorithm for Schr¨oder’s equation, The L´evy algorithm for Abel’s equation, An algorithm for B¨ottcher’s equation, Solving commutativity equations, Generalizations of Abel’s and Schr¨oder’s equations, General properties of iterative roots, Functional equations and nested radicals, Problems
Miscellaneous methods for functional equations
Polynomial equations, Power series methods, Equations involving arithmetic functions, An equation using special groups, Problems
Some closing heuristics
Appendix: Hamel bases
Hints and partial solutions to problems


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