The Theory of Distributions A Nontechnical Introduction [Paperback]

A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.This introduction to the subject of generalized functions concentrates on the essential results important to non-specialists, yet is still mathematically correct. The book is self-contained and requires no specialized knowledge of functional analysis, topological vector spaces or measure theory.This introduction to the subject of generalized functions concentrates on the essential results important to non-specialists, yet is still mathematically correct. The book is self-contained and requires no specialized knowledge of functional analysis, topological vector spaces or measure theory.This book is a self-contained introduction to the theory of distributions, sometimes called generalized functions. Most books on this subject are either intuitive or else rigorous but technically demanding. Here, by concentrating on the essential results, the authors have introduced the subject in a way that will most appeal to non-specialists, yet is still mathematically correct. Topics covered include: the Dirac delta function, generalized functions, dipoles, quadrupoles, pseudofunctions and Fourier transforms. The self-contained treatment does not require any knowledge of functional analysis or topological vector spaces; even measure theory is not needed for most of the book. The book, which can be used either to accompany a course or for self-study, is liberally supplied with exercises. It will be a valuable introduction to the theory of distributions and their applications for students or professionals in statistics, physics, engineering and economics.Preface; 1. Introduction; 2. The elements of distribution theory: Section 1. Basic Definitions and Facts; Section 2. Convolutions; 3. Examples of distributions; 4. Fourier transforms; 5. Tempered distributions; 6. Extension to higher dimensions; 7. A general definition of multiplication and convolution for distributions;l#¶