On Functions and Functional Equations

✍ Scribed by Smital, J

• Publisher: CRC Press
• Year: 2020
• Tongue: English
• Leaves: 165
• Edition: First edition
• Category: Library

✦ Synopsis

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. Functional equations in several variables. Iterations. Applications of iterations. Functional equations in one variable.

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Preface......Page 8
Table of Contents......Page 6
1.1 Elementary Properties of Functions......Page 10
1.2 Continuous Functions......Page 16
1.3 Derivative of a Function......Page 20
2.1 Introduction......Page 29
2.2 The Cauchy Functional Equation and Related Equations......Page 36
2.3 Other Important Types of Equations......Page 47
2.4 Applications of functional Equations in Several Variables......Page 54
2.5 Discontinuous Solution of the Cauchy Functional Equation......Page 59
2.6 Concluding Remarks......Page 64
3.1 Introduction......Page 67
3.2 Fixed Points......Page 72
3.3 Cycles......Page 81
3.4 Chaos......Page 93
3.5 Stability......Page 103
3.6 Concluding Remarks......Page 110
4.1 Introduction......Page 113
4.2 A Discrete Model of Population Growth for a Single Biological Species......Page 115
4.3 A Discrete Model of Epidemics......Page 123
4.4 A Discrete Population Growth Model for Two Species......Page 130
5.1 Introduction......Page 133
5.2 Characteristic Mappings and Invariants......Page 137
5.3 Linear Functional Equations......Page 143
5.4 The Abel and Schröder Equations......Page 153
5.5 Concluding Remarks......Page 157
References......Page 159
Index......Page 163

✦ Subjects

Functional equations;Functions of several real variables;Iterative methods (Mathematics);MATHEMATICS / Functional Analysis;MATHEMATICS / General;Electronic books