Mathematical Modeling of Diverse Phenomena PDF Download
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Author: James Carson Howard
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 416
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Book Description
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
Author: James Carson Howard
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 416
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Book Description
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
Author: James C. Howard
Publisher:
ISBN: 9781410218605
Category : Mathematics
Languages : en
Pages : 408
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Book Description
This book is intended for those students, engineers, scientists, and applied mathematicians who find it necessary to formulate models of diverse phenomena. To facilitate the formulation of such models, some aspects of the tensor calculus will be introduced. However, no knowledge of tensors is assumed. The chief aim of this calculus is the investigation of relations that remain valid in going from one coordinate system to another. The invariance of tensor quantities with respect to coordinate transformations can be used to advantage in formulating mathematical models. As a consequence of the geometrical simplification inherent in the tensor method, the formulation of problems in curvilinear coordinate systems can be reduced to series of routine operations involving only summation and differentiation. When conventional methods are used, the form which the equations of mathematical physics assumes depends on the coordinate system used to describe the problem being studied. This dependence, which is due to the practice of expressing vectors in terms of their physical components, can be removed by the simple expedient of expressing all vectors in terms of their tensor components.
Author: Neil A. Gershenfeld
Publisher: Cambridge University Press
ISBN: 9780521570954
Category : Mathematics
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: Michael Olinick
Publisher: John Wiley & Sons
ISBN: 1118642694
Category : Mathematics
Languages : en
Pages : 594
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Book Description
Olinick’s Mathematical Models in the Social and Life Sciences concentrates not on physical models, but on models found in biology, social science, and daily life. This text concentrates on a relatively small number of models to allow students to study them critically and in depth, and balances practice and theory in its approach. Each chapter concluded with suggested projects that encourage students to build their own models, and space is set aside for historical and biographical notes about the development of mathematical models.
Author: James Sneyd
Publisher: American Mathematical Soc.
ISBN: 0821828169
Category : Medical
Languages : en
Pages : 194
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Book Description
In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective. The book is suitable for mathematicians and biologists interested in mathematical methods in biology.
Author: Jonas Hall
Publisher: John Wiley & Sons
ISBN: 1119102693
Category : Mathematics
Languages : en
Pages : 571
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Book Description
A logical problem-based introduction to the use of GeoGebra for mathematical modeling and problem solving within various areas of mathematics A well-organized guide to mathematical modeling techniques for evaluating and solving problems in the diverse field of mathematics, Mathematical Modeling: Applications with GeoGebra presents a unique approach to software applications in GeoGebra and WolframAlpha. The software is well suited for modeling problems in numerous areas of mathematics including algebra, symbolic algebra, dynamic geometry, three-dimensional geometry, and statistics. Featuring detailed information on how GeoGebra can be used as a guide to mathematical modeling, the book provides comprehensive modeling examples that correspond to different levels of mathematical experience, from simple linear relations to differential equations. Each chapter builds on the previous chapter with practical examples in order to illustrate the mathematical modeling skills necessary for problem solving. Addressing methods for evaluating models including relative error, correlation, square sum of errors, regression, and confidence interval, Mathematical Modeling: Applications with GeoGebra also includes: Over 400 diagrams and 300 GeoGebra examples with practical approaches to mathematical modeling that help the reader develop a full understanding of the content Numerous real-world exercises with solutions to help readers learn mathematical modeling techniques A companion website with GeoGebra constructions and screencasts Mathematical Modeling: Applications with GeoGebrais ideal for upper-undergraduate and graduate-level courses in mathematical modeling, applied mathematics, modeling and simulation, operations research, and optimization. The book is also an excellent reference for undergraduate and high school instructors in mathematics.
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:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 410
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Book Description
Author: Douglas D. Mooney
Publisher: American Mathematical Society
ISBN: 1470466163
Category : Mathematics
Languages : en
Pages : 453
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Book Description
The emphasis of this book lies in the teaching of mathematical modeling rather than simply presenting models. To this end the book starts with the simple discrete exponential growth model as a building block, and successively refines it. This involves adding variable growth rates, multiple variables, fitting growth rates to data, including random elements, testing exactness of fit, using computer simulations and moving to a continuous setting. No advanced knowledge is assumed of the reader, making this book suitable for elementary modeling courses. The book can also be used to supplement courses in linear algebra, differential equations, probability theory and statistics.
Author: Leah Edelstein-Keshet
Publisher: SIAM
ISBN: 9780898719147
Category : Mathematics
Languages : en
Pages : 629
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Book Description
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.
