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Generating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc. This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems. Specifically, the book discusses probability GFs (PGF), moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs. Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.
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.
This is an introductory book on discrete statistical distributions and its applications. It discusses only those that are widely used in the applications of probability and statistics in everyday life. The purpose is to give a self-contained introduction to classical discrete distributions in statistics. Instead of compiling the important formulas (which are available in many other textbooks), we focus on important applications of each distribution in various applied fields like bioinformatics, genomics, ecology, electronics, epidemiology, management, reliability, etc., making this book an indispensable resource for researchers and practitioners in several scientific fields. Examples are drawn from different fields. An up-to-date reference appears at the end of the book. Chapter 1 introduces the basic concepts on random variables, and gives a simple method to find the mean deviation (MD) of discrete distributions. The Bernoulli and binomial distributions are discussed in detail in Chapter 2. A short chapter on discrete uniform distribution appears next. The next two chapters are on geometric and negative binomial distributions. Chapter 6 discusses the Poisson distribution in-depth, including applications in various fields. Chapter 7 is on hypergeometric distribution. As most textbooks in the market either do not discuss, or contain only brief description of the negative hypergeometric distribution, we have included an entire chapter on it. A short chapter on logarithmic series distribution follows it, in which a theorem to find the kth moment of logarithmic distribution using (k-1)th moment of zero-truncated geometric distribution is presented. The last chapter is on multinomial distribution and its applications. The primary users of this book are professionals and practitioners in various fields of engineering and the applied sciences. It will also be of use to graduate students in statistics, research scholars in science disciplines, and teachers of statistics, biostatistics, biotechnology, education, and psychology.
How does data evidence matter in decision-making in healthcare? How do you implement and maintain cost effective healthcare operations? Do decision trees help to sharpen decision making? This book will answer these questions, demystifying the many questions by clearly showing how to analyse data and how to interpret the results – vital skills for anyone who will go on to work in health administration in hospitals, clinics, pharmaceutical or insurance industries. Written by an expert in health and medical informatics, this book introduces readers to the fundamentals of operational decision making by illustrating the ideas and tools to reach optimal healthcare, drawing on numerous healthcare data sets from multiple sources. Aimed at an audience of graduate students and lecturers in Healthcare Administration and Business Administration courses and heavily illustrated throughout, this book includes up-to-date concepts, new methodologies and interpretations using widely available software: Excel, Microsoft Mathematics, MathSolver and JASP.
While more and more undergraduate engineering programs are moving toward a multi-disciplinary capstone experience, there remains a need for a suitable textbook. The present text seeks to meet that need by providing a student friendly step by step template for this important and culminating academic journey beginning with the student design team's first meeting with the client to the final report and presentation. The text provides a wide range of design tools, a discussion of various design methodologies, a brief history of modern engineering, and a substantive consideration of engineering ethics. In addition, chapters are included on communication, team building and dealing with the inevitable obstacles that students encounter. Throughout the text, emphasis is placed upon the issues of environmental impact and the importance of diversity.
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.
The characterization of cultural heritage objects becomes increasingly important for conservation, restoration, dating, and authentication purposes. The use of scientific methods in archaeometry and conservation science has led to a significant broadening of the field. Scientific analysis of these objects is a challenging task due to their complex composition, artistic and historical values requiring the use of minimally invasive and nondestructive analytical procedures. This textbook summarizes scientific methods that are currently used to characterize objects of cultural heritage and archaeological artifacts. This book provides a brief description of the structure of matter at the molecular, atomic, and nuclear levels. Furthermore, it discusses the chemical and physical nature of materials from the molecular to the atomic and nuclear level as determined by the principles of quantum mechanics. Important aspects of natural and anthropogenic radioactivity that play a critical role for some of the analytical techniques are also emphasized. The textbook also provides principals and applications of spectroscopic methods for characterization of cultural heritage objects. It describes the technologies with specific examples for utilization of spectroscopic techniques in the characterization of paintings, books, coins, ceramics, and other objects. Analytic approaches that employ isotopes and determination of isotope ratios will be reviewed. General principles of imaging techniques and specific examples for utilization of these methods will also be summarized. In the later part of the book, a number of scientific techniques for the age determination of cultural heritage material and archaeological artifacts will be presented and discussed with specific examples.
There is only a very limited number of physical systems that can be exactly described in terms of simple analytic functions. There are, however, a vast range of problems which are amenable to a computational approach. This book provides a concise, self-contained introduction to the basic numerical and analytic techniques, which form the foundations of the algorithms commonly employed to give a quantitative description of systems of genuine physical interest. The methods developed are applied to representative problems from classical and quantum physics.
Pragmatism attends to the practical outcomes of what we think and do, the social community in which we practice, and the bases of experience to inform our ideas and practices. Practice theories help explain what we do as complex systems of activity. Together, pragmatism and practice theories help broaden our understanding of the nature of engineering work as a social practice having important consequences for individuals and society. The practical nature of engineering embedded in our complex social and community systems is emphasized. Of all the pragmatists John Dewey's influence on education has been the most profound.He promoted social democracy in education. Although he founded experimental schools with this as their goal of major interest, to engineering educators his promotion of problem solving through a form of inquiry is his major attraction. Its modern embodiment is problem-based learning. It requires teachers to become facilitators of learning rather than transmitters of knowledge. How, within the framework of a traditionally oriented curriculum Dewey's epistemology of inquiry-based learning might be introduced is discussed. Lonergan's basic method of the human mind underlying specialized methods offers a basis for a unified theory and pedagogy of engineering. It also provides for a conception of engineering that gives due recognition to its ethical character and to the need for engineering virtues. This knowing-based view of engineering, focused on "engineering insight," provides the basis for a core, discipline-neutral approach to engineering.It proposes an engineering education centered on norms inherent to the knowing process, specifically attentiveness and intentionality. These norms in turn provide a source for defining and developing engineering virtues and character.
Blending physics with the study of ancient Chinese science, technology, and culture is a unique and highly effective way to present the fundamentals of physics to non-science majors. Based on the author’s course at Mercer University (Georgia, U.S.), The Art of Teaching Physics with Ancient Chinese Science and Technology exposes a wide range of students to the scientific method and techniques of experimental analysis through the eyes and discoveries of ancient Chinese “polymaths” long before the European concept of the scientific method was even considered. No other book so deftly makes the connections from ancient China to Ben Franklin to Michael Faraday while teaching physics at the same time. A distinctive characteristic of this book is the detailed hands-on laboratory experiments. This first includes making a simple magnetic compass and magnetometer. Students then use the compass/magnetometer to measure the strength of the magnetic field produced by a long straight wire. The second experiment covers two different methods of mining copper to introduce students to simple chemical principles such as displacement reactions, oxidation, reduction, and electronegativity. Originally developed for non-science students in an Asian studies environment, this book provides a valuable resource for science teachers who wish to explore the historical connections largely ignored in traditional texts. When paired with Teaching Physics through Ancient Chinese Science and Technology (Marone, 2019), these two texts provide a unique means of studying selected topics traditionally found in a two-semester Physics course.