Operational Calculus: Volume 1

This edition is divided into 2 volumes, the first volume containing applications, and the second volume the theoretical treatment of operational calculus. Practical applications are given at length in addition to abstract and difficult theorems in pure mathematics. Operational functions are introduced and applied in a lengthy discussion of the wave equation, the heat equation, and the equations of telegraphy. The general theory of linear partial differential equations with constant coefficients, and the integral of an operational function are considered. This edition contains abstract mathematical theory but includes many applications of practical importance. Contents: Foreword; PART 1. Operational Algebra: - Concept and properties of a convolution of continuous functions - Theorem of Titchmarsh - Operators; PART 2. Sequences and series of operators: Sequence of operators - Series of translation operators - Difference equations - Power series; PART 3. The operational differential calculus: Operational functions and their derivatives - Exponential functions - Differential equation x"(lambda) = wx(lambda); Answers to problems; Bibliography; Index