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**
Introduction to Functional Equations by Costas Efthimiou
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**About this book :- **
**Introduction to Functional Equations ** written by
** Costas Efthimiou **

This book is an attempt to present the fundamentals of the topic at hand in a pedagogical manner, accessible to students who have a background on the theory of functions up to differentiability.
Although there are some parts of the book that use additional ideas from calculus, such parts may be omitted at first reading. In particular, the book should be useful to high school students who participate in math competitions and have an interest in International Math Olympiads (IMO).

**Book Detail :- **
** Title: ** Introduction to Functional Equations
** Edition: **
** Author(s): ** Costas Efthimiou
** Publisher: **
** Series: **
** Year: ** 2010
** Pages: ** 362
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: ** US

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**Book Contents :- **
**Introduction to Functional Equations ** written by
** Costas Efthimiou **
cover the following topics.
**Functions**

Sets, Relations, Functions, Limits & Continuity, Differentiation, Solved Problems
**Functional Relations Primer**

The Notion of Functional Relations, Beginning Problems
**Equations for Arithmetic Functions**

The Notion of Difference Equations, Multiplicative Functions, Linear Difference Equations, Solved Problems
** Equations Reducing to Algebraic Systems**

Solved Problems, Group Theory in Functional Equations
**Cauchy’s Equations**

First Cauchy Equation, Second Cauchy Equation, Third Cauchy Equation, Fourth Cauchy Equation, Solved Problems
** Cauchy’s NQR-Method**

The NQR-method, Solved Problems
** Equations for Trigonometric Functions**

Characterization of Sine and Cosine, D’Alembert-Poisson I Equation, D’Alembert-Poisson II Equation, Solved Problems
**Pexider, Vincze & Wilson Equations**

First Pexider Equation, Second Pexider Equation, Third Pexider Equation, Fourth Pexider Equation, Vincze Functional Equations, Wilson Functional Equations, Solved Problems
**Vector and Matrix Variables**

Cauchy & Pexider Type Equations, Solved Problems
**Systems of Equations**

Solved Problems
**Less Than Continuity**

Imposing Weaker Conditions, Non-Continuous Solutions, Solved Problems
** More Than Continuity**

Differentiable Functions, Analytic Functions, Stronger Conditions as a Tool
**Functional Equations for Polynomials**

Fundamentals, Symmetric Polynomials, More on the Roots of Polynomials, Solved Problems
**Conditional Functional Equations**

The Notion of Conditional Equations, An Example
** Functional Inequalities**

Useful Concepts and Facts Solved Problems
**Iterations**

The Need for New Methods, Iterates, Orbits, Fixed Points, and Cycles, Fixed Points: Discussion, Cycles: Discussion, From Iterations to Difference Equations, Solved Problems, A Taste of Chaos
**Solving by Invariants & Linearization**

Constructing Solutions, Linear Equations, The Abel and Schr ¨oder Equations, Linearization, Solved Problems
**More on Fixed Points**

Solved Problems
**Miscellaneous Problems**

Integral Functional Equations, Problems Solved by Functional Relations, Assortment of Problems
**Unsolved Problems**

Functions, Problems That Can Be Solved Using Functions, Arithmetic Functions, Functional Equations With Parameters, Functional Equations with No Parameters, Fixed Points and Cycles, Existence of Solutions, Systems of Functional Equations, Conditional Functional Equations, Polynomials, Functional Inequalities, Functional Equations Containing Derivatives, Functional Relations Containing Integrals

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**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

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**SHORTCUT TRICKS (Prime Number):- **

- Find the prime number from 1 to 100 just in 5 second (MATH PRIME NUMBER SHORTCUT TRICK from 1 to 100 number) ?
- Find a large number "A" is prime number or not (MATH PRIME NUMBER SHORTCUT TRICK By using Square Root method) ?
- Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ?