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Ordinary Differential Equations And Boundary Value Problems Volume I Advanced Ordinary Differential Equations
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Book Synopsis Ordinary Differential Equations And Boundary Value Problems - Volume I: Advanced Ordinary Differential Equations by : John R Graef
Download or read book Ordinary Differential Equations And Boundary Value Problems - Volume I: Advanced Ordinary Differential Equations written by John R Graef and published by World Scientific. This book was released on 2018-02-13 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book.The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well.Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems.Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs.
Book Synopsis Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems by : Graef John R
Download or read book Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems written by Graef John R and published by World Scientific. This book was released on 2018-09-18 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.
Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Book Synopsis Elementary Differential Equations and Boundary Value Problems by : William E. Boyce
Download or read book Elementary Differential Equations and Boundary Value Problems written by William E. Boyce and published by John Wiley & Sons. This book was released on 2017-08-21 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Book Synopsis Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by : A.K. Aziz
Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Book Synopsis Classical Methods in Ordinary Differential Equations by : Stuart P. Hastings
Download or read book Classical Methods in Ordinary Differential Equations written by Stuart P. Hastings and published by American Mathematical Soc.. This book was released on 2011-12-15 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed. The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years. Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.
Book Synopsis Advanced Ordinary Differential Equations by : Kurt Otto Friedrichs
Download or read book Advanced Ordinary Differential Equations written by Kurt Otto Friedrichs and published by CRC Press. This book was released on 1965 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Equations with Boundary Value Problems by : John C. Polking
Download or read book Differential Equations with Boundary Value Problems written by John C. Polking and published by Prentice Hall. This book was released on 2002 with total page 938 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text strikes a balance between the traditional and the modern. It combines the traditional material with a modern systems emphasis, offering flexibility of use that should allow faculty at a variety of institutions to use the book.
Book Synopsis Ordinary Differential Equations by : Wolfgang Walter
Download or read book Ordinary Differential Equations written by Wolfgang Walter and published by Springer Science & Business Media. This book was released on 2013-03-11 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
Book Synopsis Elementary Differential Equations and Boundary Value Problems by : William E. Boyce
Download or read book Elementary Differential Equations and Boundary Value Problems written by William E. Boyce and published by . This book was released on 1965 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revision of Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Like previous editions, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations and Boundary Value Problems as they apply to engineering and the sciences. A perennial best seller designed for engineers and scientists who need to use Elementary Differential Equations in their work and studies. Covers all the essential topics on differential equations, including series solutions, Laplace transforms, systems of equations, numerical methods and phase plane methods. Offers clear explanations detailed with many current examples. Before you buy, make sure you are getting the best value and all the learning tools you'll need to succeed in your course. If your professor requires eGrade Plus, you can purchase it here, with your text at no additional cost. With this special eGrade Plus package you get the new text- - no highlighting, no missing pages, no food stains- - and a registration code to eGrade Plus, a suite of effective learning tools to help you get a better grade. All this, in one convenient package! eGrade Plus gives you: A complete online version of the textbook Over 500 homework questions from the text rendered algorithmically with full hints and solutions Chapter Reviews, which summarize the main points and highlight key ideas in each chapter Student Solutions Manual Technology Manuals for Maple, Mathematica, and MatLa Link to JustAsk! eGradePlus is a powerful online tool that provides students with an integrated suite of teaching and learning resources and an online version of the text in one easy-to-use website.
Book Synopsis Ordinary Differential Equations in Theory and Practice by : Robert Mattheij
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 408 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.
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 2015-04-29 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.
Book Synopsis Handbook of Differential Equations: Ordinary Differential Equations by : A. Canada
Download or read book Handbook of Differential Equations: Ordinary Differential Equations written by A. Canada and published by Elsevier. This book was released on 2006-08-21 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
Book Synopsis Boundary Value Problems by : David L. Powers
Download or read book Boundary Value Problems written by David L. Powers and published by Academic Press. This book was released on 2006 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- Chapter 0. Ordinary Differential Equations -- Chapter 1. Fourier Series and Integrals -- Chapter 2. The Heat Equation -- Chapter 3. The Wave Equation -- Chapter 4. The Potential Equation -- Chapter 5. Higher Dimensions & Other Coordinates.
Book Synopsis Ordinary and Partial Differential Equations by : Ravi P. Agarwal
Download or read book Ordinary and Partial Differential Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2008-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
Book Synopsis Elementary Differential Equations and Boundary Value Problems by : William E. Boyce
Download or read book Elementary Differential Equations and Boundary Value Problems written by William E. Boyce and published by Wiley Global Education. This book was released on 2017-05-10 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Book Synopsis Applied Differential Equations with Boundary Value Problems by : Vladimir Dobrushkin
Download or read book Applied Differential Equations with Boundary Value Problems written by Vladimir Dobrushkin and published by CRC Press. This book was released on 2017-10-19 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Differential Equations with Boundary Value Problems 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. This new edition of the author’s popular textbook adds coverage of boundary value problems. 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.
