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Author : John Villadsen
Publisher : Prentice Hall
ISBN 13 : 9780138222055
Total Pages : 446 pages
Book Rating : 4.2/5 (22 download)
Download or read book Solution of Differential Equation Models by Polynomial Approximation written by John Villadsen and published by Prentice Hall. This book was released on 1978 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : T.P. Dreyer
Publisher : Routledge
ISBN 13 : 1351430696
Total Pages : 190 pages
Book Rating : 4.3/5 (514 download)
Download or read book Modelling with Ordinary Differential Equations written by T.P. Dreyer and published by Routledge. This book was released on 2017-09-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.
Author : Daniele Funaro
Publisher : Springer
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.:/5 (43 download)
Download or read book Polynomial Approximation of Differential Equations written by Daniele Funaro and published by Springer. This book was released on 1992 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods. In the last few decades, there has been a growing interest in this subject. As a matter offact, spectral methods provide a competitive alternative to other standard approximation techniques, for a large variety of problems. Initial ap plications were concerned with the investigation of periodic solutions of boundary value problems using trigonometric polynomials. Subsequently, the analysis was extended to algebraic polynomials. Expansions in orthogonal basis functions were preferred, due to their high accuracy and flexibility in computations. The aim of this book is to present a preliminary mathematical background for be ginners who wish to study and perform numerical experiments, or who wish to improve their skill in order to tackle more specific applications. In addition, it furnishes a com prehensive collection of basic formulas and theorems that are useful for implementations at any level of complexity. We tried to maintain an elementary exposition so that no experience in functional analysis is required.
Author : Frank R. Giordano
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 790 pages
Book Rating : 4.3/5 (97 download)
Download or read book Differential Equations written by Frank R. Giordano and published by Addison Wesley Publishing Company. This book was released on 1991 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text takes a strong mathematical modeling approach. By integrating modeling throughout the text, the authors provide a better intuitive understanding of the concepts presented. They also take what students learned in calculus and apply it to real-world problems. The text is loaded with relevant applications, many of which are engineering-oriented. The text includes coverage of phase-plane analysis and control systems.
Author : Gregory Baker
Publisher : World Scientific Publishing Company
ISBN 13 : 9814656992
Total Pages : 392 pages
Book Rating : 4.8/5 (146 download)
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.
Author : V. K. Dzyadyk
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110944693
Total Pages : 332 pages
Book Rating : 4.1/5 (19 download)
Download or read book Approximation Methods for Solutions of Differential and Integral Equations written by V. K. Dzyadyk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Approximation Methods for Solutions of Differential and Integral Equations".
Author : Martin Braun
Publisher : Springer Science & Business Media
ISBN 13 : 1461254272
Total Pages : 390 pages
Book Rating : 4.4/5 (612 download)
Download or read book Differential Equation Models written by Martin Braun and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.
Author : Charles Roberts
Publisher : CRC Press
ISBN 13 : 1498776108
Total Pages : 492 pages
Book Rating : 4.4/5 (987 download)
Download or read book Elementary Differential Equations written by Charles Roberts and published by CRC Press. This book was released on 2018-12-13 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Differential Equations, Second Edition is written with the knowledge that there has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage. This second edition has been created to address these changes and help instructors facilitate new teaching methods and the latest tools, which includes computers. The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers in teaching elementary or ordinary differential equations. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package. Features: Focuses on numerical methods and computing to generate solutions Features extensive coverage of nonlinear differential equations and nonlinear systems Includes software programs to solve problems in the text which are located on the author's website Contains a wider variety of non-mathematical models than any competing textbook This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines and other sciences. They also will find that the textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations.
Author : Paul W. Davis
Publisher :
ISBN 13 :
Total Pages : 712 pages
Book Rating : 4.F/5 ( download)
Download or read book Differential Equations written by Paul W. Davis and published by . This book was released on 1999 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: For undergraduate engineering and science courses in Differential Equations. This progressive text on differential equations utilizes MATLAB's state-of-the-art computational and graphical tools right from the start to help students probe a variety of mathematical models. Ideas are examined from four perspectives: geometric, analytic, numeric, and physical. Students are encouraged to develop problem-solving skills and independent judgment as they derive models, select approaches to their analysis, and find answers to the original, physical questions. Both qualitative and algebraic tools are stressed.*Balancing the qualitative with the algebraic, the text exposes students in the first two chapters to fundamental qualitative ides such as direction fields, steady states, stability, etc. Then graphical interpretation, analytic solutions, and numerical tools are developed to allow students to examine nonlinear problems and systems or equations. This is done in conjunction with covering the most important traditional, analytic methods*Many exercises are posed from the physical perspective of the models under study in order to nurture students' ability to easily shift between theoretical/m
Author : Kenneth Eriksson
Publisher : Cambridge University Press
ISBN 13 : 9780521567381
Total Pages : 558 pages
Book Rating : 4.5/5 (673 download)
Download or read book Computational Differential Equations written by Kenneth Eriksson and published by Cambridge University Press. This book was released on 1996-09-05 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
Author : Edward Layer
Publisher : Springer Science & Business Media
ISBN 13 : 3642560989
Total Pages : 177 pages
Book Rating : 4.6/5 (425 download)
Download or read book Modelling of Simplified Dynamical Systems written by Edward Layer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems involving synthesis of mathematical models of various physical systems, making use of these models in practice and verifying them qualitatively has - come an especially important area of research since more and more physical - periments are being replaced by computer simulations. Such simulations should make it possible to carry out a comprehensive analysis of the various properties of the system being modelled. Most importantly its dynamic properties can be - dressed in a situation where this would be difficult or even impossible to achieve through a direct physical experiment. To carry out a simulation of a real, phy- cally existing system it is necessary to have its mathematical description; the s- tem being described mathematically by equations, which include certain variables, their derivatives and integrals. If a single independent variable is sufficient in - der to describe the system, then derivatives and integrals with respect to only that variable will appear in the equations. Differentiation of the equation allows the integrals to be eliminated and produces an equation which includes derivatives with respect to only one independent variable i. e. an ordinary differential equation. In practice, most physical systems can be described with sufficient accuracy by linear differential equations with time invariant coefficients. Chapter 2 is devoted to the description of models by such equations, with time as the independent va- able.
Author :
Publisher :
ISBN 13 : 9814468169
Total Pages : pages
Book Rating : 4.8/5 (144 download)
Download or read book Modeling By Nonlinear Differential Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vladimir A. Dobrushkin
Publisher : CRC Press
ISBN 13 : 1000606244
Total Pages : 706 pages
Book Rating : 4.0/5 (6 download)
Download or read book Applied Differential Equations written by Vladimir A. Dobrushkin and published by CRC Press. This book was released on 2022-09-21 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book started as a collection of lecture notes for a course in differential equations taught by the Division of Applied Mathematics at Brown University. To some extent, it is a result of collective insights given by almost every instructor who taught such a course over the last 15 years. Therefore, the material and its presentation covered in this book were practically tested for many years. This text is designed for a two-semester sophomore or junior level course in differential equations. It offers novel approaches in presentation and utilization of computer capabilities. This text intends to provide a solid background in differential equations for students majoring in a breadth of fields. Differential equations are described in the context of applications. The author stresses differential equations constitute an essential part of modeling by showing their applications, including numerical algorithms and syntax of the four most popular software packages. Students learn how to formulate a mathematical model, how to solve differential equations (analytically or numerically), how to analyze them qualitatively, and how to interpret the results. In writing this textbook, the author aims to assist instructors and students through: Showing a course in differential equations is essential for modeling real-life phenomena Stressing the mastery of traditional solution techniques and presenting effective methods, including reliable numerical approximations Providing qualitative analysis of ordinary differential equations. The reader should get an idea of how all solutions to the given problem behave, what are their validity intervals, whether there are oscillations, vertical or horizontal asymptotes, and what is their long-term behavior The reader will learn various methods of solving, analysis, visualization, and approximation, exploiting the capabilities of computers Introduces and employs MapleTM, Mathematica®, MatLab®, and Maxima This textbook facilitates the development of the student’s skills to model real-world problems Ordinary and partial differential equations is a classical subject that has been studied for about 300 years. The beauty and utility of differential equations and their application in mathematics, biology, chemistry, computer science, economics, engineering, geology, neuroscience, physics, the life sciences, and other fields reaffirm their inclusion in myriad curricula. A great number of examples and exercises make this text well suited for self-study or for traditional use by a lecturer in class. Therefore, this textbook addresses the needs of two levels of audience, the beginning and the advanced.
Author :
Publisher : Academic Press
ISBN 13 : 9780080955834
Total Pages : 322 pages
Book Rating : 4.9/5 (558 download)
Download or read book Numerical Solution of Ordinary Differential Equations written by and published by Academic Press. This book was released on 1971-03-31 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Author : R. M. M. Mattheij
Publisher : SIAM
ISBN 13 : 9780898718270
Total Pages : 697 pages
Book Rating : 4.7/5 (182 download)
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 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.
Author : A Sinha
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
ISBN 13 : 1842659774
Total Pages : 224 pages
Book Rating : 4.8/5 (426 download)
Download or read book Applied Differential Equations written by A Sinha and published by ALPHA SCIENCE INTERNATIONAL LIMITED. This book was released on 2013-04-23 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Differential Equations discusses the Legendre and Bessel Differential equations and its solutions. Various properties of Legendre Polynomials as well as Legendre function and Bessel functions in part one. The second order Partial Differential equation of three types is studied and the technique to solve with the separation of variables technique called Fourier's Method have been discussed in the second part. In the Appendix some applications of the Heat Equation are discussed to Model the Environment. NEW TO THE SECOND EDITION:Chapter on Matlab Solution to ODE, PDE and SDE as an appendix
Author : Robert Mattheij
Publisher : SIAM
ISBN 13 : 9780898719178
Total Pages : 423 pages
Book Rating : 4.7/5 (191 download)
Download or read book Ordinary Differential Equations in Theory and Practice written by Robert Mattheij and published by SIAM. This book was released on 1996-01-01 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained. Audience: the book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.
