Mathematical Models And Methods For Real World Systems
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Mathematical Models and Methods for Real World Systems by K.M. Furati,Abul Hasan Siddiqi Pdf
Mathematics does not exist in isolation but is linked inextricably to the physical world. At the 2003 International Congress of Industrial and Applied Mathematics, leading mathematicians from around the globe gathered for a symposium on the "Mathematics of Real World Problems," which focused on furthering the establishment and dissemination of thos
Methods of Mathematical Modelling by Thomas Witelski,Mark Bowen Pdf
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Modelling Nature by Edward Gillman,Michael Gillman Pdf
This short textbook introduces students to the concept of describing natural systems using mathematical models. We highlight the variety of ways in which natural systems lend themselves to mathematical description and the importance of models in revealing fundamental processes. The process of science via the building, testing and use of models (theories) is described and forms the structure of the book. The book covers a broad range from the molecular to ecosystems and whole-Earth phenomena. Themes running through the chapters include scale (temporal and spatial), change (linear and nonlinear), emergent phenomena and uncertainty. Mathematical descriptions are kept to a minimum and we illustrate mechanisms and results in graphical form wherever possible. Essential mathematical details are described fully, with the use of boxes. The mathematics supports but does not lead the text.
Modern Mathematical Models, Methods and Algorithms for Real World Systems by A. H. Siddiqi,Iain S. Duff,Ole Christensen Pdf
This is presentation of the diverse uses and applications of contemporary mathematics in real world systems. Distinguished international scholars have contributed a total of twenty chapters discussing practical applications of mathematical theory across a range of disciplines, from financial markets to DNA sequencing from meteorology to economics in agriculture. This book will be a boon to advanced mathematicians, whether academic or professional, who are looking for real world applications for their theories. It is an outstanding collection of articles on mathematics for the new millennium.
Mathematical Modelling, Optimization, Analytic and Numerical Solutions by Pammy Manchanda,René Pierre Lozi,Abul Hasan Siddiqi Pdf
This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.
A Primer on Mathematical Modelling by Alfio Quarteroni,Paola Gervasio Pdf
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 https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.
Mathematical and Statistical Models and Methods in Reliability by V.V. Rykov,N. Balakrishnan,M.S. Nikulin Pdf
The book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by renowned experts in the field of reliability, the contributions cover a wide range of applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation. Mathematical and Statistical Models and Methods in Reliability is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.
Handbook of Real-World Applications in Modeling and Simulation by John A. Sokolowski,Catherine M. Banks Pdf
Introduces various modeling and simulation methods and paradigms that are used to explain and solve the predominant challenges facing society Handbook of Real-World Applications in Modeling and Simulation provides a thorough explanation of modeling and simulation in the most useful, current, and predominant applied areas of transportation, homeland security, medicine, operational research, military science, and business modeling. Offering a cutting-edge and accessible presentation, this book discusses how and why the presented domains have become leading applications of modeling and simulation techniques. Contributions from leading academics and researchers integrate modeling and simulation theories, methods, and data to analyze challenges that involve technological and social issues. The book begins with an introduction that explains why modeling and simulation is a reliable analysis assessment tool for complex systems problems. Subsequent chapters provide an orientation to various modeling and simulation methods and paradigms that are used to explain and solve the predominant challenges across real-world applied domains. Additionally, the handbook: Provides a practical one-stop reference on modeling and simulation and contains an accessible introduction to key concepts and techniques Introduces, trains, and prepares readers from statistics, mathematics, engineering, computer science, economics, and business to use modeling and simulation in their studies and research Features case studies that are representative of fundamental areas of multidisciplinary studies and provides a concise look at the key concepts of modeling and simulation Contains a collection of original ideas on modeling and simulation to help academics and practitioners develop a multifunctional perspective Self-contained chapters offer a comprehensive approach to explaining each respective domain and include sections that explore the related history, theory, modeling paradigms, and case studies. Key terms and techniques are clearly outlined, and exercise sets allow readers to test their comprehension of the presented material. Handbook of Real-World Applications in Modeling and Simulation is an essential reference for academics and practitioners in the areas of operations research, business, management science, engineering, statistics, mathematics, and computer science. The handbook is also a suitable supplement for courses on modeling and simulation at the graduate level.
Mathematical Modelling and Optimization of Engineering Problems by J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu Pdf
This book presents recent developments in modelling and optimization of engineering systems and the use of advanced mathematical methods for solving complex real-world problems. It provides recent theoretical developments and new techniques based on control, optimization theory, mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena including latest technologies such as additive manufacturing. Specific topics covered in detail include combinatorial optimization, flow and heat transfer, mathematical modelling, energy storage and management policy, artificial intelligence, optimal control, modelling and optimization of manufacturing systems.
Methods and Models in Mathematical Programming by S. A. MirHassani,F. Hooshmand Pdf
This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.
Modeling Life by Alan Garfinkel,Jane Shevtsov,Yina Guo Pdf
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
Mathematical Modeling of Earth's Dynamical Systems by Rudy Slingerland,Lee Kump Pdf
A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html
Mathematical Modelling by D. N. P. Murthy,N. W. Page,Ervin Y. Rodin Pdf
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.
Mathematical Modeling by Christof Eck,Harald Garcke,Peter Knabner Pdf
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.
An Introduction to Mathematical Modeling by Edward A. Bender Pdf
Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.