Download or read book Differential Equations as Models in Science and Engineering written by Gregory Baker and published by World Scientific Publishing Company. This book was released on 2016-07-25 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook develops a coherent view of differential equations by progressing through a series of typical examples in science and engineering that arise as mathematical models. All steps of the modeling process are covered: formulation of a mathematical model; the development and use of mathematical concepts that lead to constructive solutions; validation of the solutions; and consideration of the consequences. The volume engages students in thinking mathematically, while emphasizing the power and relevance of mathematics in science and engineering. There are just a few guidelines that bring coherence to the construction of solutions as the book progresses through ordinary to partial differential equations using examples from mixing, electric circuits, chemical reactions and transport processes, among others. The development of differential equations as mathematical models and the construction of their solution is placed center stage in this volume.
Download or read book Differential Equations written by Courtney Brown and published by SAGE. This book was released on 2007-05-18 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Differential Equations: A Modeling Approach' explains the mathematics and theory of differential equations. Graphical methods of analysis are emphasized over formal proofs, making the text even more accessible for newcomers to the subject matter.
Download or read book Partial Differential Equations written by Roland Glowinski and published by Springer Science & Business Media. This book was released on 2008-06-26 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.
Download or read book Modelling with Ordinary Differential Equations written by Alfio Borzì and published by CRC Press. This book was released on 2020-04-13 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available
Download or read book Differential Equations as Models in Science and Engineering written by Gregory Richard Baker and published by . This book was released on 2016 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling Differential Equations in Biology written by Clifford Henry Taubes and published by Cambridge University Press. This book was released on 2008-01-17 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a very successful one-semester course taught at Harvard, this text teaches students in the life sciences how to use differential equations to help their research. It needs only a semester's background in calculus. Ideas from linear algebra and partial differential equations that are most useful to the life sciences are introduced as needed, and in the context of life science applications, are drawn from real, published papers. It also teaches students how to recognize when differential equations can help focus research. A course taught with this book can replace the standard course in multivariable calculus that is more usually suited to engineers and physicists.
Download or read book Differential Equations as Models in Science and Engineering written by Gregory Baker and published by . This book was released on 2013 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling with It Stochastic Differential Equations written by E. Allen and published by Springer Science & Business Media. This book was released on 2007-03-08 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.
Download or read book Modeling by Nonlinear Differential Equations written by Paul Edgar Phillipson and published by World Scientific. This book was released on 2009 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions. Sample Chapter(s). Chapter 1: Theme and Contents of this Book (85 KB). Contents: Theme and Contents of this Book; Processes in closed and Open Systems; Dynamics of Molecular Evolution; Relaxation Oscillations; Order and Chaos; Reaction Diffusion Dynamics; Solitons; Neuron Pulse Propagation; Time Reversal, Dissipation and Conservation. Readership: Advanced undergraduates, graduate students and researchers in physics, chemistry, biology or bioinformatics who are interested in mathematical modeling.
Download or read book Modeling and Differential Equations in Biology written by T. A. Burton and published by CRC Press. This book was released on 1980-09-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Persistence in lotka-volterra models of food chains and competition; Mathematical models of humoral immune response; Mathematical models of dose and cell cycle effects in multifraction radiotherapy; Theorical and experimental investigations of microbial competition in continuous culture; A liapunov functional for a class of reaction-diffusion systems; Stochastic prey-predator relationships; Coexistence in predator-prey systems; Stability of some multispecies population models; Population dynamics in patchy environments; Limit cycles in a model of b-cell simulation; Optimal age-specific harvesting policy for a cintinuous time-population model; Models involving differential and integral equations appropriate for describing a temperature dependent predator-prey mite ecosystem on apples.
Download or read book Partial Differential Equations written by R. M. M. Mattheij and published by SIAM. This book was released on 2005-01-01 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: Textbook with a unique approach that integrates analysis and numerical methods and includes modelling to address real-life problems.
Download or read book A First Course in Differential Equations Modeling and Simulation written by Carlos A. Smith and published by CRC Press. This book was released on 2011-05-18 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for
Download or read book Differential Equations and Mathematical Biology written by D.S. Jones and published by CRC Press. This book was released on 2009-11-09 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deepen students' understanding of biological phenomenaSuitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeli
Download or read book Modeling By Nonlinear Differential Equations Dissipative And Conservative Processes written by Paul Phillipson and published by World Scientific. This book was released on 2009-09-29 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions
Download or read book A Practical Course in Differential Equations and Mathematical Modelling written by Nail H. Ibragimov and published by World Scientific. This book was released on 2009 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author?s own theoretical developments. The book ? which aims to present new mathematical curricula based on symmetry and invariance principles ? is tailored to develop analytic skills and ?working knowledge? in both classical and Lie?s methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author?s extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collge de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.
Download or read book Modelling with Differential and Difference Equations written by Glenn Fulford and published by Cambridge University Press. This book was released on 1997-06-12 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.
Download or read book Mathematical Modeling using Differential Equations and Network Theory written by Ioannis Dassios and published by MDPI. This book was released on 2020-06-23 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Issue collects the latest results on differential/difference equations, the mathematics of networks, and their applications to engineering and physical phenomena. It features nine high-quality papers that were published with original research results. The Special Issue brings together mathematicians with physicists, engineers, as well as other scientists.
