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Author | Charles Roberts | |

ISBN-10 | 9781439819098 | |

Release | 2011-06-13 | |

Pages | 600 | |

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In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing the computer into the classroom, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in teaching differential equations. Providing an even balance between theory, computer solution, and application, the text discusses the theorems and applications of the first-order initial value problem, including learning theory models, population growth models, epidemic models, and chemical reactions. It then examines the theory for n-th order linear differential equations and the Laplace transform and its properties, before addressing several linear differential equations with constant coefficients that arise in physical and electrical systems. The author also presents systems of first-order differential equations as well as linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems. The final chapter introduces techniques for determining the behavior of solutions to systems of first-order differential equations without first finding the solutions. Designed to be independent of any particular software package, the book includes a CD-ROM with the software used to generate the solutions and graphs for the examples. The appendices contain complete instructions for running the software. A solutions manual is available for qualifying instructors. |

Author | Charles E. Roberts | |

ISBN-10 | UOM:39015004689231 | |

Release | 1979 | |

Pages | 400 | |

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Ordinary differential equations has been writing in one form or another for most of life. You can find so many inspiration from Ordinary differential equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Ordinary differential equations book for free. |

Author | Lennart Edsberg | |

ISBN-10 | 9781119018469 | |

Release | 2015-09-16 | |

Pages | 288 | |

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Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations. |

Author | Mark McKibben | |

ISBN-10 | 9781466557079 | |

Release | 2014-09-08 | |

Pages | 497 | |

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A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB® GUIs allows students to discover patterns and make conjectures. |

Author | D.S. Jones | |

ISBN-10 | 1420083589 | |

Release | 2009-11-09 | |

Pages | 462 | |

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Deepen students’ understanding of biological phenomena Suitable 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 modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material. New to the Second Edition A section on spiral waves Recent developments in tumor biology More on the numerical solution of differential equations and numerical bifurcation analysis MATLAB® files available for download online Many additional examples and exercises This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincaré phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator–prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases. |

Author | Charles Henry Edwards | |

ISBN-10 | 0136004385 | |

Release | 2008 | |

Pages | 575 | |

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For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new emphases that permeate the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; its focus has shifted from the traditional manual methods to new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text. |

Author | Edward A. Bender | |

ISBN-10 | 9780486137124 | |

Release | 2012-05-23 | |

Pages | 272 | |

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Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition. |

Author | Courtney Brown | |

ISBN-10 | 1412941083 | |

Release | 2007-05-18 | |

Pages | 106 | |

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Differential Equations: A Modeling Approach introduces differential equations and differential equation modeling to students and researchers in the social sciences. Key Features: - The text is accessibly written, so that students with minimal mathematical training can understand all of the basic concepts and techniques presented. - The author uses social sciences examples to illustrate the relevance of differential equation modeling to readers. - Readers can use graphical methods to produce penetrating analysis of differential equation systems. - Linear and nonlinear model specifications are explained from a social science perspective. Most interesting differential equation models are nonlinear, and readers need to know how to specify and work with such models in the social sciences. |

Author | Vladimir A. Dobrushkin | |

ISBN-10 | 9781498728355 | |

Release | 2014-12-16 | |

Pages | 731 | |

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A Contemporary Approach to Teaching Differential Equations Applied Differential Equations: An Introduction presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. Designed for a two-semester undergraduate course, the text offers a true alternative to books published for past generations of students. It enables students majoring in a range of fields to obtain a solid foundation in differential equations. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results. |

Author | Belkacem Said-Houari | |

ISBN-10 | 9783319257358 | |

Release | 2016-01-11 | |

Pages | 212 | |

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This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included.The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. |

Author | Sergio E. Serrano | |

ISBN-10 | 0988865211 | |

Release | 2016-07-01 | |

Pages | 250 | |

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An introduction to ordinary differential equations and systems of ordinary differential equations, including new analytical methods to solve nonlinear equations, mathematical modeling, computer programming, computer graphics with Maple, and applications in science and engineering. ... a new textbook that will thoroughly revolutionize the teaching and learning of differential equations with the vital goal of student retention always in sight. Dr. Randolph Rach, original coauthor of the Adomian s Decomposition Method. New modern methods to solve nonlinear differential equations. Integrated, balanced presentation of model development, solution methods, computer implementation, and analysis of system s response. Designed to increase engineering and science student retention. Mathematical and computer modeling with Maple. No prior knowledge of Maple required. Emphasis on problem solving over mathematical rigorousness. Clear and simple presentation of concepts with multitude of examples: 125 solved examples, 70 computer programs, 146 proposed problems, 17 illustrations, 118 computer graphs, answers to problems, detailed bibliography. Preference of general, systematic, analytical methods over complex numerical methods. Self contained. Except for calculus, all necessary background is included." |

Author | E. C. Zachmanoglou | |

ISBN-10 | 9780486132174 | |

Release | 2012-04-20 | |

Pages | 432 | |

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This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers. |

Author | Uri M. Ascher | |

ISBN-10 | 9780898716528 | |

Release | 2008-09-04 | |

Pages | 395 | |

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Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems. |

Author | Sze-Bi Hsu | |

ISBN-10 | 9789814452922 | |

Release | 2013-06-07 | |

Pages | 312 | |

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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 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. |

Author | Carmen Chicone | |

ISBN-10 | 9780128041543 | |

Release | 2016-09-24 | |

Pages | 878 | |

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An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested |

Author | Marcelo Epstein | |

ISBN-10 | 9783319552125 | |

Release | 2017-05-15 | |

Pages | 255 | |

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This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry. |

Author | Jagat Narain Kapur | |

ISBN-10 | 812240006X | |

Release | 1988-01-01 | |

Pages | 259 | |

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Each Chapter Of The Book Deals With Mathematical Modelling Through One Or More Specified Techniques. Thus There Are Chapters On Mathematical Modelling Through Algebra, Geometry, Trigonometry And Calculus, Through Ordinary Differential Equations Of First And Second Order, Through Systems Of Differential Equations, Through Difference Equations, Through Partial Differential Equations, Through Functional Equations And Integral Equations, Through Delay-Differential, Differential-Difference And Integro-Differential Equations, Through Calculus Of Variations And Dynamic Programming, Through Graphs, Through Mathematical Programming, Maximum Principle And Maximum Entropy Principle.Each Chapter Contains Mathematical Models From Physical, Biological, Social, Management Sciences And Engineering And Technology And Illustrates Unity In Diversity Of Mathematical Sciences.The Book Contains Plenty Of Exercises In Mathematical Modelling And Is Aimed To Give A Panoramic View Of Applications Of Modelling In All Fields Of Knowledge. It Contains Both Probabilistic And Deterministic Models.The Book Presumes Only The Knowledge Of Undergraduate Mathematics And Can Be Used As A Textbook At Senior Undergraduate Or Post-Graduate Level For A One Or Two- Semester Course For Students Of Mathematics, Statistics, Physical, Social And Biological Sciences And Engineering. It Can Also Be Useful For All Users Of Mathematics And For All Mathematical Modellers. |