This book aims at improving the mathematical modelling skills of users by enhancing the ability to understand, connect, apply and use the mathematical concepts to the problem at hand. This book provides the readers with an in-depth knowledge of the various categories/classes of research problems that professionals, researchers and students might encounter following which the applications of appropriate mathematical models is explained with the help of case studies. The book is targeted at academicians, researchers, students and professionals who belong to all engineering disciplines.
Foundations of Mathematical Modeling and Analysis for Engineering develops linear system theory at a level appropriate for first-year graduate and advanced undergraduate engineering students. It demonstrates the role of linear theory in developing analytical solutions to linear algebraic, ordinary-, and partial-differential equations, which provide the foundation for describing and advancing our understanding of physical systems through mathematical modeling. It provides the mathematics foundation for learning and research within engineering and many scientific disciplines. This book provides the mathematical foundation for entry into graduate-level courses in engineering, applied mathematics, and any of the foundational sciences. Students will learn to determine all solutions to entire classes of linear algebraic, ordinary-, and partial-differential equations. They will learn principles for formulating, organizing, and solving linear subsystems that are important elements within linear and nonlinear mathematical models. - Serves as an extensive toolbox for graduate engineering students, covering both foundational and complex mathematical concepts essential for advanced studies - Emphasizes real-world applications of mathematical models, bolstering problem-solving skills through worked examples and end-of-chapter exercises - Aids the transition from undergraduate to graduate studies, ensuring comprehensive understanding and application of the mathematical concepts in advanced engineering coursework
The critical step in the use of mathematics for solving real world problems is the building of a suitable mathematical model. This book advocates a novel approach to the teaching of the building process for mathematical models, with emphasis on the art as well as the science aspects. Using a case study approach, the book teaches the mathematical modelling process in a comprehensive framework, presenting an overview of the concepts and techniques needed for modelling. The book is structured in three parts; the first dealing with the science aspect; the second dealing with the art aspects; and the third combining self learning exercises for the student and supplementary resource material for the instructor.
The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful. The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition. Review of first edition: "The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. ... Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. ... One of the best features of the book is the abundant number of exercises found at the end of each chapter. ... I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers." Joe Latulippe, The Mathematical Association of America, December, 2009
This book has come into being as a result ofthe author's lectures on mathematical modelling rendered to the students, BS and MS degree holders specializing in applied mathematics and computer science and to post-graduate students in exact sciences of the Nizhny Novgorod State University after N.!. Lobatchevsky. These lectures are adapted and presented as a single whole ab out mathematical models and modelling. This new course of lectures appeared because the contemporary Russian educational system in applied mathematics rested upon a combination of fundamental and applied mathematics training; this way of training oriented students upon solving only the exactly stated mathematical problems, and thus there was created a certain estrangement to the most essential stages and sides of real solutions for applied problems, such as thinking over and deeply piercing the essence of a specific problem and its mathematical statement. This statement embraces simplifications, adopted idealizations and creating a mathematical model, its correction and matching the results obtained against a real system. There also existed another main objective, namely to orient university graduates in their future research not only upon purely mathematical issues but also upon comprehending and widely applying mathematics as a universal language of contemporary exact science, and mathematical modelling as a powerful me ans for studying nature, engineering and human society.
A graduate level text, this book presents a unique combination of theoretical mathematics and engineering applications. It demonstrates the relationship between advanced mathematics and engineering principles, introduces engineering mathematics at a theoretical level, and includes functional analysis topics such as vector spaces, inner products, and norms and develops advanced mathematical methods from this foundation. The author does not focus on proving theorems but on the application of the theorems to the solution of engineering problems. In sum, the book provides an overview of the principles and techniques of advanced mathematics as applied to mechanical engineering problems.
This book is one-stop shop which offers essential information one must know and can implement in real-time business expansions to solve engineering problems in various disciplines. It will also help us to make future predictions and decisions using AI algorithms for engineering problems. Machine learning and optimizing techniques provide strong insights into novice users. In the era of big data, there is a need to deal with data science problems in multidisciplinary perspective. In the real world, data comes from various use cases, and there is a need of source specific data science models. Information is drawn from various platforms, channels, and sectors including web-based media, online business locales, medical services studies, and Internet. To understand the trends in the market, data science can take us through various scenarios. It takes help of artificial intelligence and machine learning techniques to design and optimize the algorithms. Big data modelling and visualization techniques of collected data play a vital role in the field of data science. This book targets the researchers from areas of artificial intelligence, machine learning, data science and big data analytics to look for new techniques in business analytics and applications of artificial intelligence in recent businesses.
"Written through the eyes of an engineer, this book offers readers an introduction to the field that looks at how engineers apply science and technology to solve problems facing society. It first focuses on how engineers represent and solve engineering problems and then describes some of the different kinds of mathematical models that are used. Readers will also find a whole section dedicated to MATLAB, an integrated environment for technical computing."--Publisher's website.
The subject of the book is the "know-how" of applied mathematical modelling: how to construct specific models and adjust them to a new engineering environment or more precise realistic assumptions; how to analyze models for the purpose of investigating real life phenomena; and how the models can extend our knowledge about a specific engineering process. Two major sources of the book are the stock of classic models and the authors' wide experience in the field. The book provides a theoretical background to guide the development of practical models and their investigation. It considers general modelling techniques, explains basic underlying physical laws and shows how to transform them into a set of mathematical equations. The emphasis is placed on common features of the modelling process in various applications as well as on complications and generalizations of models. The book covers a variety of applications: mechanical, acoustical, physical and electrical, water transportation and contamination processes; bioengineering and population control; production systems and technical equipment renovation. Mathematical tools include partial and ordinary differential equations, difference and integral equations, the calculus of variations, optimal control, bifurcation methods, and related subjects.
The central question addressed in Foundations for the Future in Mathematics Education is this: What kind of understandings and abilities should be emphasized to decrease mismatches between the narrow band of mathematical understandings and abilities that are emphasized in mathematics classrooms and tests, and those that are needed for success beyond school in the 21st century? This is an urgent question. In fields ranging from aeronautical engineering to agriculture, and from biotechnologies to business administration, outside advisors to future-oriented university programs increasingly emphasize the fact that, beyond school, the nature of problem-solving activities has changed dramatically during the past twenty years, as powerful tools for computation, conceptualization, and communication have led to fundamental changes in the levels and types of mathematical understandings and abilities that are needed for success in such fields. For K-12 students and teachers, questions about the changing nature of mathematics (and mathematical thinking beyond school) might be rephrased to ask: If the goal is to create a mathematics curriculum that will be adequate to prepare students for informed citizenship—as well as preparing them for career opportunities in learning organizations, in knowledge economies, in an age of increasing globalization—how should traditional conceptions of the 3Rs be extended or reconceived? Overall, this book suggests that it is not enough to simply make incremental changes in the existing curriculum whose traditions developed out of the needs of industrial societies. The authors, beyond simply stating conclusions from their research, use results from it to describe promising directions for a research agenda related to this question. The volume is organized in three sections: *Part I focuses on naturalistic observations aimed at clarifying what kind of “mathematical thinking” people really do when they are engaged in “real life” problem solving or decision making situations beyond school. *Part II shifts attention toward changes that have occurred in kinds of elementary-but-powerful mathematical concepts, topics, and tools that have evolved recently—and that could replace past notions of “basics” by providing new foundations for the future. This section also initiates discussions about what it means to “understand” the preceding ideas and abilities. *Part III extends these discussions about meaning and understanding—and emphasizes teaching experiments aimed at investigating how instructional activities can be designed to facilitate the development of the preceding ideas and abilities. Foundations for the Future in Mathematics Education is an essential reference for researchers, curriculum developers, assessment experts, and teacher educators across the fields of mathematics and science education.
