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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
Author(s): Costas Efthimiou
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Book Contents :-
Introduction to Functional Equations written by Costas Efthimiou cover the following topics.
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
First Cauchy Equation, Second Cauchy Equation, Third Cauchy Equation, Fourth Cauchy Equation, Solved Problems
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
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
Useful Concepts and Facts Solved Problems
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
Integral Functional Equations, Problems Solved by Functional Relations, Assortment of 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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