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On Functions and Functional Equations introduces the main topics in iteration theory and the theory of functional equations with emphasis on applications in the fields of mathematics, physics, biology, chemistry, and electronics and mechanical engineering. The book contains many classical results as well as important, more recent results. It also includes numerous exercise and some problems that have yet to be resolved. The book is accessible to readers having a secondary level mathematical education.
Table of Contents
FUNCTIONS Elementary properties of functions Continuous functions Derivatives of a function
FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES Introduction The Cauchy functional equation and related equations Other important types of equations Applications of functional equations in several variables Discontinuous solution of the Cauchy functional equation Concluding remarks
APPLICATIONS OF ITERATIONS Introduction A discrete model of population growth for a single biological species A discrete model of epidemics A discrete population growth model for two species
FUNCTIONAL EQUATIONS IN ONE VARIABLE Introduction Characteristic mappings and invariants Linear functional equations The Abel and Schröder equations Concluding remarks
"… takes the reader from the familiar ideas of undergraduate mathematics to the newest ideas in its subject without losing either the integrity of the subject or the reader's comprehension … I heartily recommend this book." -Australian Physicist
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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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