Mathematical Modeling of Natural Phenomena PDF Download

Author: Ranis Ibragimov
Publisher:
ISBN: 9781536129786
Category : Differential equations
Languages : en
Pages :

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Book Description

Author: Ranis Ibragimov
Publisher:
ISBN: 9781536129779
Category : Differential equations
Languages : en
Pages : 0

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Book Description
Mathematical modeling in the form of differential equations is a branch of applied mathematics that includes topics from physics, engineering, environmental and computer science. The mathematical model is an approximate description of real processes. Mathematical modeling can be thought of as a three step process: 1) Physical situation; 2) Mathematical formulation; 3) Solution by purely operations of the mathematical problem; 4) Physical interpretation of the mathematical solution. Over the centuries, Step 2 took on a life of its own. Mathematics was studied on its own, devoid of any contact with a physical problem; this is known as pure mathematics. Applied mathematics and mathematical modeling deals with all three steps. Improvements of approximations or their extensions to more general situations may increase the complexity of mathematical models significantly. Before the 18th century, applied mathematics and its methods received the close attention of the best mathematicians who were driven by a desire to develop approximate descriptions of natural phenomena. The goal of asymptotic and perturbation methods is to find useful, approximate solutions to difficult problems that arise from the desire to understand a physical process. Exact solutions are usually either impossible to obtain or too complicated to be useful. Approximate, useful solutions are often tested by comparison with experiments or observations rather than by rigorous mathematical methods. Hence, the authors will not be concerned with rigorous proofs in this book. The derivation of approximate solutions can be done in two different ways. First, one can find an approximate set of equations that can be solved, or, one can find an approximate solution of a set of equations. Usually one must do both. Models of natural science show that the possibilities of applying differential equations for solving problems in the disciplines of the natural scientific cycle are quite wide. This book represents a unique blend of the traditional analytical and numerical methods enriched by the authors developments and applications to ocean and atmospheric sciences. The overall viewpoint taken is a theoretical, unified approach to the study of both the atmosphere and the oceans. One of the key features in this book is the combination of approximate forms of the basic mathematical equations of mathematical modeling with careful and precise analysis. The approximations are required to make any progress possible, while precision is needed to make the progress meaningful. This combination is often the most elusive for student to appreciate. This book aims to highlight this issue by means of accurate derivation of mathematical models with precise analysis and MATLAB applications. This book is meant for undergraduate and graduate students interested in applied mathematics, differential equations and mathematical modeling of real world problems. This book might also be interested in experts working in the field of physics concerning the ocean and atmosphere.

Author: Angela Slavova
Publisher: Cambridge Scholars Publishing
ISBN: 1527507351
Category : Mathematics
Languages : en
Pages : 220

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Book Description
This book presents a study of neuroscience models and natural phenomena, such as tsunami waves and tornados. The first part discusses various mathematical models of tsunamis, including the Korteweg–de Vries equation, shallow water equations and the Camassa–Holm equation (CH). In order to study the dynamics of these models, the text uses the Cellular Nonlinear Networks (CNN) approach to discretize the governing equation using a suitable mathematical grid. The second part discusses some of the models arising in the field of neuroscience. It examines the Fitzhugh-Nagumo systems, which are very important for understanding the qualitative nature of nerve impulse propagation. The volume will be of interest to a wide-ranging audience, including PhD students, mathematicians, physicists, engineers and specialists in the domain of nonlinear waves and their applications.

Author: John Adam
Publisher: Princeton University Press
ISBN: 1400841011
Category : Mathematics
Languages : en
Pages : 408

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Book Description
From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

Author: Neil A. Gershenfeld
Publisher: Cambridge University Press
ISBN: 9780521570954
Category : Science
Languages : en
Pages : 268

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Book Description
This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area. The text is complemented by extensive worked problems.

Author: Robert S. Wolff
Publisher: Springer
ISBN: 9780387978093
Category : Computers
Languages : en
Pages : 374

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Book Description
by David C Nagel In the last five years visualization has gone from the lab to become a desktop technology for many scientists. Images and 3-D renderings of data sets and mathematical models have evolved from the high-priced hardware and customized software of graphics professionals to low-cost, off-the-shelf commercial software running on personal computers. fu such, scientific visualization has taken its place beside mathematical modeling as an everyday means of interacting with one's data. This has significantly changed both the amount and the quality of information that scientists are able to extract from raw data, and has effectively established a new paradigm for scientific computing. In addi tion, new, low-cost hardware and software technologies such as CD-ROMs, digital video, and Apple's QuickTime time-based media of image and and compression technologies have enabled large amounts animation data to be easily accessible to the average researcher or teacher through the personal computer. However, little has been done in the way of providing a context within which the researcher or teacher could learn which approaches might be best suited for a given problem. Furthermore, most scientists are unfamiliar with the terminology and concepts in modern computer graphics, which simply steepens the learning curve for them to apply the new technologies to their work. fu a result, researchers and teachers are not yet taking full advantage of the new paradigm.

Author: Eyal Kolman
Publisher: Springer Science & Business Media
ISBN: 3540880763
Category : Computers
Languages : en
Pages : 108

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Book Description
This book details the state-of-the-art in knowledge-based neurocomputing. It introduces a novel fuzzy-rule base known as Fuzzy All-permutations Rule-Base (FARB) and presents new connections between artificial neural networks and FARB.

Author: Christof Eck
Publisher: Springer
ISBN: 3319551612
Category : Mathematics
Languages : en
Pages : 519

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Book Description
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.

Author: Edward Gillman
Publisher: CABI
ISBN: 1786393107
Category : Science
Languages : en
Pages : 281

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Book Description
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.

Author: Cristiana J. Silva
Publisher: Frontiers Media SA
ISBN: 2832546064
Category : Science
Languages : en
Pages : 135

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Book Description
Mathematical modeling of real life phenomena is a powerful tool in analyzing and describing their dynamical behavior. These models can be optimized and controlled using appropriate optimization methods and optimal control theory. Different characterization techniques are used to explain a real natural phenomenon by numerical simulations or experimental approximations.