Generating Functions In Engineering And The Applied Sciences

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Generating Functions in Engineering and the Applied Sciences

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031794109
Total Pages : 99 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Generating Functions in Engineering and the Applied Sciences by : Rajan Chattamvelli

Download or read book Generating Functions in Engineering and the Applied Sciences written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-05-31 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generating Functions in Engineering and the Applied Sciences

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 303121143X
Total Pages : 129 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Generating Functions in Engineering and the Applied Sciences by : Rajan Chattamvelli

Download or read book Generating Functions in Engineering and the Applied Sciences written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2023-01-01 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generatingfunctionology

Author : Herbert S. Wilf
Publisher : Elsevier
ISBN 13 : 1483276635
Total Pages : 193 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Generatingfunctionology by : Herbert S. Wilf

Download or read book Generatingfunctionology written by Herbert S. Wilf and published by Elsevier. This book was released on 2014-05-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

Theory and Applications of the Generating Functions: Pure Mathematics and Applied Science

Author : Stefano Spezia
Publisher :
ISBN 13 : 9781774698747
Total Pages : 0 pages
Book Rating : 4.6/5 (987 download)

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Book Synopsis Theory and Applications of the Generating Functions: Pure Mathematics and Applied Science by : Stefano Spezia

Download or read book Theory and Applications of the Generating Functions: Pure Mathematics and Applied Science written by Stefano Spezia and published by . This book was released on 2023-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generating functions have various applications in many branches of mathematics and sciences, representing a widely used and powerful tool for solving problems. In combinatorics, they allow for obtaining a compact representation of discrete structures and the investigation of several properties of the sequences they generate, i.e. their asymptotic growth. Theory and Applications of the Generating Functions: Pure Mathematics and Applied Science book provides the mathematical basis and application examples: generating functions, infinite series, and asymptotic methods.

Obtaining Generating Functions

Author : Elna B. McBride
Publisher : Springer Science & Business Media
ISBN 13 : 364287682X
Total Pages : 109 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Obtaining Generating Functions by : Elna B. McBride

Download or read book Obtaining Generating Functions written by Elna B. McBride and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the study of methods of obtaining generating functions. It is an expository work at the level of the beginning graduate student. The first part of Chapter I gives the reader the necessary definitions and basic concepts. The fundamental method of direct summation is explained and illustrated. The second part of Chapter I deals with the methods developed by Rainville. These methods are based principally on inventive manipulation of power series. Weisner's group-theoretic method is explained in detail in Chapter II and is further illustrated in Chapter III. When this method is applicable, it yields a set of at least three generating functions. In Chapter II for the Laguerre polynomials six generating functions were found. Truesdell's method is studied in Chapter IV. For a given set of functions {fez, an the success of this method depends on the existence of certain transformations. If fez, a) can be transformed into F(z, a) such that a a-; F(z, a)=F(z, a+ 1), or if fez, a) can be transformed into G(z, a) such that a a-; G(z, a)=G(z, a-I), then from each transformed function a generating function can be obtained. Truesdell's method for obtaining the transformed functions does not require any ingenuity on the user's part. Truesdell has shown how these simple results may be exploited to generate more complicated results by means of specified, systematic, and general processes. His method of obtaining generating functions is only one of these results.

Discrete Distributions in Engineering and the Applied Sciences

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031024257
Total Pages : 205 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Discrete Distributions in Engineering and the Applied Sciences by : Rajan Chattamvelli

Download or read book Discrete Distributions in Engineering and the Applied Sciences written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-06-01 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Data-Guided Healthcare Decision Making

Author : Ramalingam Shanmugam
Publisher : Cambridge University Press
ISBN 13 : 1009212001
Total Pages : 529 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Data-Guided Healthcare Decision Making by : Ramalingam Shanmugam

Download or read book Data-Guided Healthcare Decision Making written by Ramalingam Shanmugam and published by Cambridge University Press. This book was released on 2023-05-31 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Engineering Design

Author : George D. Catalano
Publisher : Springer Nature
ISBN 13 : 3031020901
Total Pages : 125 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Engineering Design by : George D. Catalano

Download or read book Engineering Design written by George D. Catalano and published by Springer Nature. This book was released on 2022-05-31 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Ann Saterbak
Publisher : Springer Nature
ISBN 13 : 3031020936
Total Pages : 223 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Introduction to Engineering Design by : Ann Saterbak

Download or read book Introduction to Engineering Design written by Ann Saterbak and published by Springer Nature. This book was released on 2022-06-01 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Scientific Analysis of Cultural Heritage Objects

Author : Michael Wiescher
Publisher : Springer Nature
ISBN 13 : 3031020871
Total Pages : 228 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Scientific Analysis of Cultural Heritage Objects by : Michael Wiescher

Download or read book Scientific Analysis of Cultural Heritage Objects written by Michael Wiescher and published by Springer Nature. This book was released on 2022-05-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Numerical Methods for the Physical Sciences

Author : Colm T. Whelan
Publisher : Springer Nature
ISBN 13 : 3031020855
Total Pages : 148 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis An Introduction to Numerical Methods for the Physical Sciences by : Colm T. Whelan

Download or read book An Introduction to Numerical Methods for the Physical Sciences written by Colm T. Whelan and published by Springer Nature. This book was released on 2022-05-31 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Philosophy and Engineering Education

Author : Russell Korte
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1636393187
Total Pages : 76 pages
Book Rating : 4.6/5 (363 download)

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Book Synopsis Philosophy and Engineering Education by : Russell Korte

Download or read book Philosophy and Engineering Education written by Russell Korte and published by Morgan & Claypool Publishers. This book was released on 2022-02-23 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Art of Teaching Physics with Ancient Chinese Science and Technology

Author : Matt Marone
Publisher : Springer Nature
ISBN 13 : 303102088X
Total Pages : 157 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Art of Teaching Physics with Ancient Chinese Science and Technology by : Matt Marone

Download or read book The Art of Teaching Physics with Ancient Chinese Science and Technology written by Matt Marone and published by Springer Nature. This book was released on 2022-05-31 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Case Studies in Forensic Physics

Author : Gregory A. DiLisi
Publisher : Springer Nature
ISBN 13 : 3031020863
Total Pages : 146 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Case Studies in Forensic Physics by : Gregory A. DiLisi

Download or read book Case Studies in Forensic Physics written by Gregory A. DiLisi and published by Springer Nature. This book was released on 2022-06-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a forensics-style re-examination of several historical events. The purpose of these studies is to afford readers the opportunity to apply basic principles of physics to unsolved mysteries and controversial events in order to settle the historical debate. We identify nine advantages of using case studies as a pedagogical approach to understanding forensic physics. Each of these nine advantages is the focus of a chapter of this book. Within each chapter, we show how a cascade of unlikely events resulted in an unpredictable catastrophe and use introductory-level physics to analyze the outcome. Armed with the tools of a good forensic physicist, the reader will realize that the historical record is far from being a set of agreed upon immutable facts; instead, it is a living, changing thing that is open to re-visitation, re-examination, and re-interpretation.

Biologically Inspired Design

Author : Torben A. Lenau
Publisher : Springer Nature
ISBN 13 : 303102091X
Total Pages : 95 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Biologically Inspired Design by : Torben A. Lenau

Download or read book Biologically Inspired Design written by Torben A. Lenau and published by Springer Nature. This book was released on 2022-06-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the existence of all life forms on our planet is currently in grave danger from the climate emergency caused by Homo sapiens, the words "sustainability" and "eco-responsibility" have entered the daily-use vocabularies of scientists, engineers, economists, business managers, industrialists, capitalists, and policy makers. Normal activities undertaken for the design of products and systems in industrialisms must be revamped. As the bioworld is a great resource for eco-responsible design activities, an overview of biologically inspired design is presented in this book in simple terms for anyone with even high-school education. Beginning with an introduction to the process of design in industry, the book presents the bioworld as a design resource along with the rationale for biologically inspired design. Problem-driven and solution-driven approaches for biologically inspired design are described next. The last chapter is focused on biologically inspired design for environment.

Nanotechnology Past and Present

Author : Deb Newberry
Publisher : Springer Nature
ISBN 13 : 3031020847
Total Pages : 83 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Nanotechnology Past and Present by : Deb Newberry

Download or read book Nanotechnology Past and Present written by Deb Newberry and published by Springer Nature. This book was released on 2022-06-01 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nanoscience and nanotechnology, the application of the research-based nanoscale science, have changed significantly over the last three and a half decades. The “bucky” ball, 60 carbon atoms arranged like a soccer ball, and an often-used symbol of nanotechnology, was discovered in 1985 and 4 years later scientists at IBM were able to manipulate xenon atoms on a surface. In the intervening years, nanotechnology has evolved from a singly focused research topic to an understanding that infiltrates every aspect of science and engineering disciplines. In addition, nanotechnology, and both naturally occurring and engineered nanomaterials, have become the focus of legal, environmental, and application and regulation disciplines. The first portion of this text serves as an introduction to nanotechnology: the history, mathematical concepts, and instruments required to study and manipulate the world at the atomic scale. The later portion of the text discusses the connectivity of nanotechnology to the more traditional scientific disciplines as well as emerging technologies. This text can serve as an introduction to the nanoscale for science, computer science, and engineering disciplines. It can also provide a valuable foundation for disciplines such as industrial hygiene, architecture, sociology, ethics, and the humanities. There does not exist an educational discipline, market segment, or career avenue which will not be impacted by nanotechnology.

Integrated Process Design and Operational Optimization via Multiparametric Programming

Author : Baris Burnak
Publisher : Springer Nature
ISBN 13 : 3031020898
Total Pages : 242 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Integrated Process Design and Operational Optimization via Multiparametric Programming by : Baris Burnak

Download or read book Integrated Process Design and Operational Optimization via Multiparametric Programming written by Baris Burnak and published by Springer Nature. This book was released on 2022-06-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive optimization-based theory and framework that exploits the synergistic interactions and tradeoffs between process design and operational decisions that span different time scales. Conventional methods in the process industry often isolate decision making mechanisms with a hierarchical information flow to achieve tractable problems, risking suboptimal, even infeasible operations. In this book, foundations of a systematic model-based strategy for simultaneous process design, scheduling, and control optimization is detailed to achieve reduced cost and improved energy consumption in process systems. The material covered in this book is well suited for the use of industrial practitioners, academics, and researchers. In Chapter 1, a historical perspective on the milestones in model-based design optimization techniques is presented along with an overview of the state-of-the-art mathematical tools to solve the resulting complex problems. Chapters 2 and 3 discuss two fundamental concepts that are essential for the reader. These concepts are (i) mixed integer dynamic optimization problems and two algorithms to solve this class of optimization problems, and (ii) developing a model based multiparametric programming model predictive control. These tools are used to systematically evaluate the tradeoffs between different time-scale decisions based on a single high-fidelity model, as demonstrated on (i) design and control, (ii) scheduling and control, and (iii) design, scheduling, and control problems. We present illustrative examples on chemical processing units, including continuous stirred tank reactors, distillation columns, and combined heat and power regeneration units, along with discussions of other relevant work in the literature for each class of problems.