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Introduction to Functional Equations by Costas Efthimiou

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INTRODUCTION TO FUNCTIONAL EQUATIONS written by COSTAS EFTHIMIOU Department of Physics, UNIVERSITY OF CENTRAL FLORIDA This is an other great mathematics book 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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