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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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  • Free
  • English
  • PDF 108
  • Page 18