An Introduction to Mathematical Modeling Book

An Introduction to Mathematical Modeling

  • Author : Edward A. Bender
  • Publisher : Courier Corporation
  • Release Date : 2012-05-23
  • Genre: Mathematics
  • Pages : 272
  • ISBN 10 : 9780486137124

An Introduction to Mathematical Modeling Excerpt :

Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Mathematical Modelling Book

Mathematical Modelling

  • Author : Seyed M. Moghadas
  • Publisher : John Wiley & Sons
  • Release Date : 2018-07-24
  • Genre: Mathematics
  • Pages : 192
  • ISBN 10 : 9781119484028

Mathematical Modelling Excerpt :

An important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.

Principles of Mathematical Modeling Book

Principles of Mathematical Modeling

  • Author : Clive Dym
  • Publisher : Elsevier
  • Release Date : 2004-08-10
  • Genre: Mathematics
  • Pages : 303
  • ISBN 10 : 9780080470283

Principles of Mathematical Modeling Excerpt :

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics. Serves as an introductory text on the development and application of mathematical models Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems Offers more than 360 problems, providing ample opportunities for practice Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences Uses straightforward language and explanations that make modeling easy to understand and apply New to this Edition: A more systematic approach to mathematical modeling, outlining ten specific principles Expanded and reorganized chapters that flow in an increasing level of complexity Several new problems and updated applications Expanded figure captions that provide more information Impr

Mathematical Modelling Book

Mathematical Modelling

  • Author : Reinhard Illner
  • Publisher : American Mathematical Soc.
  • Release Date : 2005
  • Genre: Mathematics
  • Pages : 196
  • ISBN 10 : 9780821836507

Mathematical Modelling Excerpt :

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. In this book the authors have succeeded in demonstrating just how enjoyable this subject can be. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive; others are more modest. The text was designed to be suitable for a one-term course for advanced undergraduates on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions.

A Primer on Mathematical Modelling Book

A Primer on Mathematical Modelling

  • Author : Alfio Quarteroni
  • Publisher : Springer Nature
  • Release Date : 2020-10-09
  • Genre: Mathematics
  • Pages : 238
  • ISBN 10 : 9783030445416

A Primer on Mathematical Modelling Excerpt :

In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from This book is addressed to any student interested in learning how to construct and apply mathematical models.

Mathematical Modelling Book

Mathematical Modelling

  • Author : Seppo Pohjolainen
  • Publisher : Springer
  • Release Date : 2016-07-14
  • Genre: Mathematics
  • Pages : 242
  • ISBN 10 : 9783319278360

Mathematical Modelling Excerpt :

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Mathematical Modelling Book

Mathematical Modelling

  • Author : Simon Serovajsky
  • Publisher : CRC Press
  • Release Date : 2021-11-24
  • Genre: Mathematics
  • Pages : 466
  • ISBN 10 : 9781000503975

Mathematical Modelling Excerpt :

Mathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented. Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.

A Biologist s Guide to Mathematical Modeling in Ecology and Evolution Book
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A Biologist s Guide to Mathematical Modeling in Ecology and Evolution

  • Author : Sarah P. Otto
  • Publisher : Princeton University Press
  • Release Date : 2011-09-19
  • Genre: Science
  • Pages : 744
  • ISBN 10 : 9781400840915

A Biologist s Guide to Mathematical Modeling in Ecology and Evolution Excerpt :

Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available

Mathematical Modeling Book

Mathematical Modeling

  • Author : Christof Eck
  • Publisher : Springer
  • Release Date : 2017-04-11
  • Genre: Mathematics
  • Pages : 509
  • ISBN 10 : 9783319551616

Mathematical Modeling Excerpt :

Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Mathematical Modelling and Applications Book

Mathematical Modelling and Applications

  • Author : Gloria Ann Stillman
  • Publisher : Springer
  • Release Date : 2017-11-05
  • Genre: Education
  • Pages : 647
  • ISBN 10 : 9783319629681

Mathematical Modelling and Applications Excerpt :

This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e.g., those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e.g., history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.

Mathematical Modelling Techniques Book

Mathematical Modelling Techniques

  • Author : Rutherford Aris
  • Publisher : Courier Corporation
  • Release Date : 2012-06-29
  • Genre: Technology & Engineering
  • Pages : 288
  • ISBN 10 : 9780486138893

Mathematical Modelling Techniques Excerpt :

Highly useful volume discusses the types of models, how to formulate and manipulate them for best results. Numerous examples.

A Concrete Approach to Mathematical Modelling Book

A Concrete Approach to Mathematical Modelling

  • Author : Mike Mesterton-Gibbons
  • Publisher : John Wiley & Sons
  • Release Date : 2011-02-14
  • Genre: Mathematics
  • Pages : 620
  • ISBN 10 : 9781118030646

A Concrete Approach to Mathematical Modelling Excerpt :

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists ofselected books that have been made more accessible to consumers inan effort to increase global appeal and general circulation. Withthese new unabridged softcover volumes, Wiley hopes to extend thelives of these works by making them available to future generationsof statisticians, mathematicians, and scientists. " . . . [a] treasure house of material for students and teachersalike . . . can be dipped into regularly for inspiration and ideas.It deserves to become a classic." —London Times Higher Education Supplement "The author succeeds in his goal of serving the needs of theundergraduate population who want to see mathematics in action, andthe mathematics used is extensive and provoking." —SIAM Review "Each chapter discusses a wealth of examples ranging from oldstandards . . . to novelty . . . each model is developedcritically, analyzed critically, and assessed critically." —Mathematical Reviews A Concrete Approach to Mathematical Modelling providesin-depth and systematic coverage of the art and science ofmathematical modelling. Dr. Mesterton-Gibbons shows how themodelling process works and includes fascinating examples fromvirtually every realm of human, machine, natural, and cosmicactivity. Various models are found throughout the book, includinghow to determine how fast cars drive through a tunnel, how manyworkers industry should employ, the length of a supermarketcheckout line, and more. With detailed explanations, exercises, andexamples demonstrating real-life applications in diverse fields,this book is the ultimate guide for students and professionals inthe social sciences, life sciences, engineering, statistics,economics, politics, business and management sciences, and everyother discipline in which mathematical modelling plays a role.

Mathematical Modelling of Contemporary Electricity Markets Book

Mathematical Modelling of Contemporary Electricity Markets

  • Author : Athanasios Dagoumas
  • Publisher : Academic Press
  • Release Date : 2021-01-30
  • Genre: Business & Economics
  • Pages : 442
  • ISBN 10 : 9780128218396

Mathematical Modelling of Contemporary Electricity Markets Excerpt :

Mathematical Modelling of Contemporary Electricity Markets reviews major methodologies and tools to accurately analyze and forecast contemporary electricity markets in a ways that is ideal for practitioner and academic audiences. Approaches include optimization, neural networks, genetic algorithms, co-optimization, econometrics, E3 models and energy system models. The work examines how new challenges affect power market modeling, including discussions of stochastic renewables, price volatility, dynamic participation of demand, integration of storage and electric vehicles, interdependence with other commodity markets and the evolution of policy developments (market coupling processes, security of supply). Coverage addresses all major forms of electricity markets: day-ahead, forward, intraday, balancing, and capacity. Provides a diverse body of established techniques suitable for modeling any major aspect of electricity markets Familiarizes energy experts with the quantitative skills needed in competitive electricity markets Reviews market risk for energy investment decisions by stressing the multi-dimensionality of electricity markets

Introduction to Mathematical Modeling Book

Introduction to Mathematical Modeling

  • Author : Mayer Humi
  • Publisher : CRC Press
  • Release Date : 2017-09-19
  • Genre: Mathematics
  • Pages : 500
  • ISBN 10 : 9781498728027

Introduction to Mathematical Modeling Excerpt :

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

Mathematical Modelling Book

Mathematical Modelling

  • Author : John Berry
  • Publisher : Gulf Professional Publishing
  • Release Date : 1995-06-17
  • Genre: Mathematics
  • Pages : 157
  • ISBN 10 : 9780340614044

Mathematical Modelling Excerpt :

Assuming virtually no prior knowledge, Modular Mathematics encourages the reader to develop and solve real models, as well as looking at traditional examples. Accessible and concise, it contains tutorial problems, case studies and exercises.