Non-Local Partial Differential Equations for Engineering and Biology
Non-Local Partial Differential Equations for Engineering and Biology

Author: Nikos I. Kavallaris

Publisher: Springer

Published: 2017-11-28

Total Pages: 310

ISBN-13: 3319679449

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This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.

Nonlinear Ordinary Differential Equations
Nonlinear Ordinary Differential Equations

Author: R. Grimshaw

Publisher: Routledge

Published: 2017-10-19

Total Pages: 342

ISBN-13: 135142808X

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Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.

Differential Equations and Their Applications
Differential Equations and Their Applications

Author: M. Braun

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 733

ISBN-13: 1475749694

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For the past several years the Division of Applied Mathematics at Brown University has been teaching an extremely popular sophomore level differential equations course. The immense success of this course is due primarily to two fac tors. First, and foremost, the material is presented in a manner which is rigorous enough for our mathematics and ap plied mathematics majors, but yet intuitive and practical enough for our engineering, biology, economics, physics and geology majors. Secondly, numerous case histories are given of how researchers have used differential equations to solve real life problems. This book is the outgrowth of this course. It is a rigorous treatment of differential equations and their appli cations, and can be understood by anyone who has had a two semester course in Calculus. It contains all the material usually covered in a one or two semester course in differen tial equations. In addition, it possesses the following unique features which distinguish it from other textbooks on differential equations.

Ordinary Differential Equations with Applications
Ordinary Differential Equations with Applications

Author: Sze-Bi Hsu

Publisher: World Scientific

Published: 2006

Total Pages: 258

ISBN-13: 9812563199

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During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).This useful book, which is based around the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook or as a valuable resource for researchers.

Differential Equations and Dynamical Systems
Differential Equations and Dynamical Systems

Author: Lawrence Perko

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 530

ISBN-13: 1468402498

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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.

Fuzzy Differential Equations and Applications for Engineers and Scientists
Fuzzy Differential Equations and Applications for Engineers and Scientists

Author: S. Chakraverty

Publisher: CRC Press

Published: 2016-11-25

Total Pages: 138

ISBN-13: 1315355531

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Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique work?provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.

Differential Equations with Applications in Biology, Physics, and Engineering
Differential Equations with Applications in Biology, Physics, and Engineering

Author: Jerome A. Goldstein

Publisher: Routledge

Published: 2017-10-05

Total Pages: 353

ISBN-13: 1351455184

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Suitable as a textbook for a graduate seminar in mathematical modelling, and as a resource for scientists in a wide range of disciplines. Presents 22 lectures from an international conference in Leibnitz, Austria (no date mentioned), explaining recent developments and results in differential equatio

Modern Elementary Differential Equations
Modern Elementary Differential Equations

Author: Richard Bellman

Publisher: Courier Corporation

Published: 1995-01-01

Total Pages: 260

ISBN-13: 9780486686431

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Designed to introduce students to the theory and applications of differential equations and to help them formulate scientific problems in terms of such equations, this undergraduate-level text emphasizes applications to problems in biology, economics, engineering, and physics. This edition also includes material on discontinuous solutions, Riccati and Euler equations, and linear difference equations.

DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS
DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS

Author: ZAFAR AHSAN

Publisher: PHI Learning Pvt. Ltd.

Published: 2016-07-01

Total Pages: 654

ISBN-13: 8120352696

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Primarily intended for the undergraduate students of mathematics, physics and engineering, this text gives in-depth coverage of differential equations and the methods for solving them. The book begins with the definitions, the physical and geometric origins of differential equations, and the methods for solving the first order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher order differential equations and their applications to telecommunications, civil engineering, cardiology and detection of diabetes, as also the methods of solving simultaneous differential equations and their applications. Besides, the book provides a detailed discussion on Laplace transforms and their applications, partial differential equations and their applications to vibration of stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications. The book, which is a happy fusion of theory and application, would also be useful to postgraduate students.NEW TO THIS EDITION • New sections on: (a) Equations reducible to linear partial differential equations (b) General method for solving the second order non-linear partial differential equations (Monge’s Method) (c) Lagrange’s equations of motion • Number of solved examples in Chapters 5, 7, 8, 9 and 10.