Generating Functions In Engineering And The Applied Sciences

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Generating Functions in Engineering and the Applied Sciences

Author: Rajan Chattamvelli
language: en
Publisher: Springer Nature
Release Date: 2022-05-31
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.
Random Variables for Scientists and Engineers

Author: Rajan Chattamvelli
language: en
Publisher: Springer Nature
Release Date: 2024-05-27
This book provides an introductory overview of random variables and their transformations. The authors approach the topic with statistics students in mind, along with researchers in various fields who are interested in data analysis. The book begins with by defining and explaining mathematical expectation. The authors then discuss transformations of random variables, including distribution functions and special functions. The book also covers joint probability distribution and its applications. The authors have updated and expanded upon their writing on these topics, which they originally covered in their previous book, Statistics for Scientists and Engineers.
Introduction to Engineering Design

Introduction to Engineering Design is a practical, straightforward workbook designed to systematize the often messy process of designing solutions to open-ended problems. IFrom learning about the problem to prototyping a solution, this workbook guides developing engineers and designers through the iterative steps of the engineering design process. Created in a freshman engineering design course over ten years, this workbook has been refined to clearly guide students and teams to success. Together with a series of instructional videos and short project examples, the workbook has space for teams to execute the engineering design process on a challenge of their choice. Designed for university students as well as motivated learners, the workbook supports creative students as they tackle important problems. IIntroduction to Engineering Design is designed for educators looking to use project-based engineering design in their classroom.