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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
** Edition: **
** Author(s): ** Christopher G. Small
** Publisher: ** Springer
** Series: **
** 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**
**Bibliography**
**Index**

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**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

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