On Functions and Functional Equations [Hardcover]

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.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

ITERATIONS
Introduction
Fixed points
Cycles
Chaos
Stability
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 Schr?der equations
Concluding remarks

REFERENCES
INDEX