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Generating Functions in Engineering and the Applied Sciences [electronic resource] / by Rajan Chattamvelli, Ramalingam Shanmugam

Author
Chattamvelli, Rajan
Published
Cham : Springer International Publishing : Imprint: Springer, 2019.
Edition
1st ed. 2019.
Physical Description
XV, 99 p. online resource
Additional Creators
Shanmugam, Ramalingam and SpringerLink (Online service)
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Contents
List of Tables -- Types of Generating Functions -- Operations on Generating Functions -- Generating Functions in Statistics -- Applications of Generating Functions -- Bibliography -- Authors' Biographies -- Index .
Summary
This is an introductory book on generating functions (GFs) and their applications. It discusses commonly encountered generating functions in engineering and applied sciences, such as ordinary generating functions (OGF), exponential generating functions (EGF), probability generating functions (PGF), etc. Some new GFs like Pochhammer generating functions for both rising and falling factorials are introduced in Chapter 2. Two novel GFs called "mean deviation generating function" (MDGF) and "survival function generating function" (SFGF), are introduced in Chapter 3. The mean deviation of a variety of discrete distributions are derived using the MDGF. The last chapter discusses a large number of applications in various disciplines including algebra, analysis of algorithms, polymer chemistry, combinatorics, graph theory, number theory, reliability, epidemiology, bio-informatics, genetics, management, economics, and statistics. Some background knowledge on GFs is often assumed for courses in analysis of algorithms, advanced data structures, digital signal processing (DSP), graph theory, etc. These are usually provided by either a course on "discrete mathematics" or "introduction to combinatorics." But, GFs are also used in automata theory, bio-informatics, differential equations, DSP, number theory, physical chemistry, reliability engineering, stochastic processes, and so on. Students of these courses may not have exposure to discrete mathematics or combinatorics. This book is written in such a way that even those who do not have prior knowledge can easily follow through the chapters, and apply the lessons learned in their respective disciplines. The purpose is to give a broad exposure to commonly used techniques of combinatorial mathematics, highlighting applications in a variety of disciplines.
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ISBN
9783031794100
9783031794117 (print)
9783031794094 (print)
9783031794124 (print)
Digital File Characteristics
text file PDF
Part Of
Springer Nature eBook
View MARC record | catkey: 47080926