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Theory Of Ordinary Differential Equations With Applications In Biology And Engineering
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Book Synopsis Theory Of Ordinary Differential Equations: With Applications In Biology And Engineering by : Ahmad Shair Et.Al
Download or read book Theory Of Ordinary Differential Equations: With Applications In Biology And Engineering written by Ahmad Shair Et.Al and published by . This book was released on 1999 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Equations with Applications in Biology, Physics, and Engineering by : Jerome A. Goldstein
Download or read book Differential Equations with Applications in Biology, Physics, and Engineering written by Jerome A. Goldstein and published by Routledge. This book was released on 2017-10-05 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Ordinary Differential Equations With Applications by : Sze-Bi Hsu
Download or read book Ordinary Differential Equations With Applications written by Sze-Bi Hsu and published by . This book was released on 2005 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Differential Equations with Applications by : Sze-Bi Hsu
Download or read book Ordinary Differential Equations with Applications written by Sze-Bi Hsu and published by World Scientific Publishing Company. This book was released on 2013-06-07 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 on 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 and as a valuable resource for researchers. This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.
Book Synopsis Differential Equation Analysis in Biomedical Science and Engineering by : William E. Schiesser
Download or read book Differential Equation Analysis in Biomedical Science and Engineering written by William E. Schiesser and published by John Wiley & Sons. This book was released on 2014-02-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear ordinary differential equations. The author’s primary focus is on models expressed as systems of ODEs, which generally result by neglecting spatial effects so that the ODE dependent variables are uniform in space. Therefore, time is the independent variable in most applications of ODE systems. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for ODEs Models as systems of ODEs with explanations of the associated chemistry, physics, biology, and physiology as well as the algebraic equations used to calculate intermediate variables Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general ODE computation through various biomolecular science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Book Synopsis The Qualitative Theory of Ordinary Differential Equations by : Fred Brauer
Download or read book The Qualitative Theory of Ordinary Differential Equations written by Fred Brauer and published by Courier Corporation. This book was released on 2012-12-11 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.
Book Synopsis Differential Equations and Mathematical Biology by : D.S. Jones
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
Book Synopsis Ordinary Differential Equations: Basics and Beyond by : David G. Schaeffer
Download or read book Ordinary Differential Equations: Basics and Beyond written by David G. Schaeffer and published by Springer. This book was released on 2016-11-10 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).
Book Synopsis Differential Equations with Applications to Biology by : Shigui Ruan
Download or read book Differential Equations with Applications to Biology written by Shigui Ruan and published by American Mathematical Soc.. This book was released on with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.
Book Synopsis Non-Local Partial Differential Equations for Engineering and Biology by : Nikos I. Kavallaris
Download or read book Non-Local Partial Differential Equations for Engineering and Biology written by Nikos I. Kavallaris and published by Springer. This book was released on 2017-11-28 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential Equations: Techniques, Theory, and Applications by : Barbara D. MacCluer
Download or read book Differential Equations: Techniques, Theory, and Applications written by Barbara D. MacCluer and published by American Mathematical Soc.. This book was released on 2019-10-02 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations: Techniques, Theory, and Applications is designed for a modern first course in differential equations either one or two semesters in length. The organization of the book interweaves the three components in the subtitle, with each building on and supporting the others. Techniques include not just computational methods for producing solutions to differential equations, but also qualitative methods for extracting conceptual information about differential equations and the systems modeled by them. Theory is developed as a means of organizing, understanding, and codifying general principles. Applications show the usefulness of the subject as a whole and heighten interest in both solution techniques and theory. Formal proofs are included in cases where they enhance core understanding; otherwise, they are replaced by informal justifications containing key ideas of a proof in a more conversational format. Applications are drawn from a wide variety of fields: those in physical science and engineering are prominent, of course, but models from biology, medicine, ecology, economics, and sports are also featured. The 1,400+ exercises are especially compelling. They range from routine calculations to large-scale projects. The more difficult problems, both theoretical and applied, are typically presented in manageable steps. The hundreds of meticulously detailed modeling problems were deliberately designed along pedagogical principles found especially effective in the MAA study Characteristics of Successful Calculus Programs, namely, that asking students to work problems that require them to grapple with concepts (or even proofs) and do modeling activities is key to successful student experiences and retention in STEM programs. The exposition itself is exceptionally readable, rigorous yet conversational. Students will find it inviting and approachable. The text supports many different styles of pedagogy from traditional lecture to a flipped classroom model. The availability of a computer algebra system is not assumed, but there are many opportunities to incorporate the use of one.
Book Synopsis Ordinary Differential Equations in the Complex Domain by : Einar Hille
Download or read book Ordinary Differential Equations in the Complex Domain written by Einar Hille and published by Courier Corporation. This book was released on 1997-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.
Book Synopsis Nonlinear Ordinary Differential Equations by : R. Grimshaw
Download or read book Nonlinear Ordinary Differential Equations written by R. Grimshaw and published by Routledge. This book was released on 2017-10-19 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Analysis of Ordinary Differential Equations by : Sanjeeva Balasuriya
Download or read book Applied Analysis of Ordinary Differential Equations written by Sanjeeva Balasuriya and published by MDPI. This book was released on 2019-11-14 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: One might say that ordinary differential equations (notably, in Isaac Newton’s analysis of the motion of celestial bodies) had a central role in the development of modern applied mathematics. This book is devoted to research articles which build upon this spirit: combining analysis with the applications of ordinary differential equations (ODEs). ODEs arise across a spectrum of applications in physics, engineering, geophysics, biology, chemistry, economics, etc., because the rules governing the time-variation of relevant fields is often naturally expressed in terms of relationships between rates of change. ODEs also emerge in stochastic models—for example, when considering the evolution of a probability density function—and in large networks of interconnected agents. The increasing ease of numerically simulating large systems of ODEs has resulted in a plethora of publications in this area; nevertheless, the difficulty of parametrizing models means that the computational results by themselves are sometimes questionable. Therefore, analysis cannot be ignored. This book comprises articles that possess both interesting applications and the mathematical analysis driven by such applications.
Book Synopsis Ordinary Differential Equations by : Jane Cronin
Download or read book Ordinary Differential Equations written by Jane Cronin and published by CRC Press. This book was released on 2007-12-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations. Requiring only a background in advanced calculus and linear algebra, the text is appropriate for advanced undergraduate and graduate students in mathematics, engineering, physics, chemistry, or biology. This third edition of a highly acclaimed textbook provides a detailed account of the Bendixson theory of solutions of two-dimensional nonlinear autonomous equations, which is a classical subject that has become more prominent in recent biological applications. By using the Poincaré method, it gives a unified treatment of the periodic solutions of perturbed equations. This includes the existence and stability of periodic solutions of perturbed nonautonomous and autonomous equations (bifurcation theory). The text shows how topological degree can be applied to extend the results. It also explains that using the averaging method to seek such periodic solutions is a special case of the use of the Poincaré method.
Book Synopsis Lectures on Differential Equations by : Philip L. Korman
Download or read book Lectures on Differential Equations written by Philip L. Korman and published by American Mathematical Soc.. This book was released on 2019-08-30 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Differential Equations provides a clear and concise presentation of differential equations for undergraduates and beginning graduate students. There is more than enough material here for a year-long course. In fact, the text developed from the author's notes for three courses: the undergraduate introduction to ordinary differential equations, the undergraduate course in Fourier analysis and partial differential equations, and a first graduate course in differential equations. The first four chapters cover the classical syllabus for the undergraduate ODE course leavened by a modern awareness of computing and qualitative methods. The next two chapters contain a well-developed exposition of linear and nonlinear systems with a similarly fresh approach. The final two chapters cover boundary value problems, Fourier analysis, and the elementary theory of PDEs. The author makes a concerted effort to use plain language and to always start from a simple example or application. The presentation should appeal to, and be readable by, students, especially students in engineering and science. Without being excessively theoretical, the book does address a number of unusual topics: Massera's theorem, Lyapunov's inequality, the isoperimetric inequality, numerical solutions of nonlinear boundary value problems, and more. There are also some new approaches to standard topics including a rethought presentation of series solutions and a nonstandard, but more intuitive, proof of the existence and uniqueness theorem. The collection of problems is especially rich and contains many very challenging exercises. Philip Korman is professor of mathematics at the University of Cincinnati. He is the author of over one hundred research articles in differential equations and the monograph Global Solution Curves for Semilinear Elliptic Equations. Korman has served on the editorial boards of Communications on Applied Nonlinear Analysis, Electronic Journal of Differential Equations, SIAM Review, an\ d Differential Equations and Applications.
Book Synopsis A Textbook on Ordinary Differential Equations by : Shair Ahmad
Download or read book A Textbook on Ordinary Differential Equations written by Shair Ahmad and published by Springer. This book was released on 2015-06-05 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.
