Operational Calculus

✍ Scribed by Jan Mikusinski

• Publisher: Pergamon Pr
• Year: 1984
• Tongue: English
• Leaves: 317
• Series: International series of monographs in pure and applied mathematics
• Edition: 2 Sub
• Category: Library

✦ Synopsis

Pure and Applied Mathematics, Volume 109: Operational Calculus, Second Edition. Volume I presents the foundations of operational calculus and its applications to physics and engineering. This book introduces the operators algebraically as a kind of fractions.

Organized into three parts, this volume begins with an overview of the concept as well as the characteristics of a convolution of continuous functions. This text then examines the transitivity, associativity, and distributivity of convolution with regard to addition. Other parts consider the methods of solving other difference equations, particularly in the field of electrical engineering, in which the variable runs over integer values only. This book discusses as well the solution of differential equations under given initial conditions. The final part deals with the characteristic properties of a derivative and provides the definition of algebraic derivative to any operators.

This book is a valuable resource for physicists, electrical engineers, mathematicians, and research workers.

✦ Table of Contents

Content:
Other Pergamon titles of interest, Page 2
Front Matter, Page 3
Copyright, Page 4
FOREWORD, Pages 10-11
FOREWORD TO THE SECOND ENGLISH EDITION, Page 11
CHAPTER I - THE CONCEPT AND PROPERTIES OF A CONVOLUTION OF CONTINUOUS FUNCTIONS, Pages 12-19
CHAPTER II - THEOREM OF TITCHMARSH, Pages 20-28
CHAPTER III - OPERATORS, Pages 29-50
CHAPTER IV - ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS, Pages 51-56
CHAPTER V - THEORY OF ELECTRIC CIRCUIT, Pages 57-108
CHAPTER VI - GENERAL SOLUTIONS OF DIFFERENTIAL EQUATIONS AND BOUNDARY PROBLEMS, Pages 109-116
CHAPTER VII - DISCONTINUOUS FUNCTIONS, Pages 117-137
CHAPTER VIII - APPLICATIONS TO THE STATICS OF BEAMS(1), Pages 138-151
CHAPTER I - SEQUENCES OF OPERATORS, Pages 152-159
CHAPTER II - SERIES OF TRANSLATION OPERATORS, Pages 160-168
CHAPTER III - DIFFERENCE EQUATIONS, Pages 169-176
CHAPTER IV - POWER SERIES, Pages 177-189
CHAPTER I - OPERATIONAL FUNCTIONS AND THEIR DERIVATIVES, Pages 190-201
CHAPTER II - EXPONENTIAL FUNCTIONS, Pages 202-208
CHAPTER III - DIFFERENTIAL EQUATION x″ (λ) = wx(λ), Pages 209-212
CHAPTER IV - VIBRATIONS OF A STRING, Pages 213-230
CHAPTER V - THE EQUATION OF HEAT, Pages 231-264
CHAPTER VI - THE EQUATION OF TELEGRAPHY, Pages 265-272
CHAPTER VII - APPLICATIONS TO CHROMATOGRAPHY(1), Pages 273-293
CHAPTER VIII - THE ALGEBRAIC DERIVATIVE, Pages 294-298
ANSWERS TO PROBLEMS, Pages 299-314
BIBLIOGRAPHY, Pages 315-317
Index, Page 318
OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS, Pages 319-321
Errata, Page 323