UID:
almahu_9947366158002882
Umfang:
1 online resource (533 p.)
ISBN:
1-282-28968-3
,
9786612289682
,
0-08-095525-8
Serie:
Mathematics in science and engineering ; 19
Inhalt:
Lectures on functional equations and their applications
Anmerkung:
Description based upon print version of record.
,
Front Cover; Lectures on Functional Equations and Their Applications; Copyright Page; Contents; Foreword to the German Edition; Foreword to the English Edition; Introduction; 0.1 Definition and Examples; 0.2 History; PART I: Equations for Functions of a Single Variable; CHAPTER 1. Equations Which Can Be Solved by Simple Substitutions; 1.1 Equations of the Form f[G(x, y)] = F[f(x), y]; 1.2 Methods of Solving Similar Types of Equations; 1.3 An Application: Scalar Product and Vector Product; CHAPTER 2. Solution of Equations by Determining the Values of the Unknown Function on a Dense Set
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2.1 Cauchy's Equations and Jensen's Equation2.2 Equations of the Type f(x + y ) = F[f(x), f (y)], Related Equations, and Generalizations; 2.3 Some Applications (Euclidean and Non-Euclidean Geometry, Mechanics, Business Mathematics, Probability Theory); 2.4 D'Alembert's Functional Equation and Its Application; 2.5 Additional Functional Equations with One Function of One Variable; CHAPTER 3. Equations with Several Unknown Functions; 3.1 Pexider's and Related Equations; 3.2 Functional Equations for the Trigonometric Functions and Related Equations
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CHAPTER 4. Reduction to Differential and Integral Equations, General Methods4.1 Integral Transformations and Reduction to Integral Equations; 4.2 Reduction to Differential Equations. Some General Methods; PART II: Equations for Functions of Several Variables; CHAPTER 5. Simple Equations; 5.1 Generalizations of Cauchy's and Similar Equations and Their Applications; 5.2 The Equations of Homogeneous Functions and Related Equations; 5.3 The Equations of the Weighted Mean; CHAPTER 6. Composite Equations; 6.1 The Translation Equation; 6.2 The Associativity Equation; 6.3 The Transitivity Equation
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6.4 The Bisymmetry Equation6.5 The Autodistributivity Equations; CHAPTER 7. Equations with Several Unknown Functions of Several Variables. Reduction to Partial Differential Equations; 7.1 Equations with Several Unknown Functions That Are Solvable by Elementary Methods; 7.2 Reduction to Partial Differential Equations and Functional Differential Equations; CHAPTER 8. Vector and Matrix Equations; 8.1 Cauchy-Pexider-Sincov Equations; 8.2. Associativity, Transformation, and Distributivity Equations; Concluding Remarks. Some Unsolved Problems; Bibliography; Author Index; Subject Index
,
English
Weitere Ausg.:
ISBN 0-12-043750-3
Sprache:
Englisch
