Fundamentals of Differential Equations and Boundary Value Problems

Author: R. Kent Nagle,E. B. Saff,Arthur David Snider

Publisher: Addison-Wesley

ISBN: 9780321145710

Category: Mathematics

Page: 896

View: 9173

Fundamentals of Differential Equations, Sixth Edition is designed for a one-semester sophomore or junior-level course. Fundamentals of Differential Equations and Boundary Value Problems, Third Edition, contains enough material for a two-semester course that covers and builds on boundary-value problems. These tried-and-true texts help students understand the methods and concepts they will need to successfully complete engineering courses. The new texts retain the features that have made previous editions successful, while integrating recent advances in teaching and learning. The Fundamentals of Differential Equations and Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory). - Chapters 4 (Linear Second Order Equations) and 5 (Introduction to Systems and Phase Plane Analysis) have been substantially rewritten and tightened. - New Group Projects have been added. - The exercises have been tightened and updated. - Applications-driven sections are included in the chapter on linear second order equations. - The chapter regarding the i
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Fundamentals of Differential Equations with Boundary Value Problems

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 149028978X

Category: Education

Page: 18

View: 2370

Facts101 is your complete guide to Fundamentals of Differential Equations with Boundary Value Problems. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
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Fundamentals of Differential Equations

Author: R. Kent Nagle,E. B. Saff,Arthur David Snider

Publisher: Addison-Wesley

ISBN: 9780321145727

Category: Mathematics

Page: 709

View: 8222

This text is in a flexible one-semester text that spans a variety of topics in the basic theory as well as applications of differential equations.
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Introduction to Partial Differential Equations

Author: Peter J. Olver

Publisher: Springer Science & Business Media

ISBN: 3319020994

Category: Mathematics

Page: 636

View: 5353

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.
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Numerical Approximation Methods for Elliptic Boundary Value Problems

Finite and Boundary Elements

Author: Olaf Steinbach

Publisher: Springer Science & Business Media

ISBN: 0387313125

Category: Mathematics

Page: 386

View: 9146

This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
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A Course in Differential Equations with Boundary Value Problems, Second Edition

Author: Stephen A. Wirkus,Randall J. Swift,Ryan Szypowski

Publisher: CRC Press

ISBN: 1498736068

Category: Mathematics

Page: 788

View: 3776

A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®,?Mathematica®, and MapleTM. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. ? Features MATLAB®,?Mathematica®, and MapleTM are incorporated at the end of each chapter. All three software packages have parallel code and exercises; There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages. Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book
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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

Author: Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell

Publisher: SIAM

ISBN: 9781611971231

Category: Boundary value problems

Page: 595

View: 4173

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.
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Fundamentals of Heat and Mass Transfer:

Author: Thirumaleshwar, M.

Publisher: Pearson Education India

ISBN: 8131798658

Category:

Page: 800

View: 5391

Fundamentals of Heat and Mass Transfer is written for senior undergraduates in engineering colleges of Indian universities, in the departments of Mechanical, Automobile, Production, Chemical, Nuclear and Aerospace Engineering. The book should also
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Differential Equations with Boundary-Value Problems

Author: Dennis G. Zill

Publisher: Cengage Learning

ISBN: 1305965795

Category: Mathematics

Page: 664

View: 5272

DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 9th Edition, strikes a balance between the analytical, qualitative, and quantitative approaches to the study of Differential Equations. This proven text speaks to students of varied majors through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, and definitions. Written in a straightforward, readable, and helpful style, the book provides a thorough overview of the topics typically taught in a first course in Differential Equations as well as an introduction to boundary-value problems and partial Differential Equations. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Partial Differential Equations of Parabolic Type

Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 0486318265

Category: Mathematics

Page: 368

View: 2783

With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.
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The Physics of Cerebrovascular Diseases

Biophysical Mechanisms of Development, Diagnosis and Therapy

Author: George J. Hademenos,Tarik F. Massoud

Publisher: Springer Science & Business Media

ISBN: 9781563965586

Category: Science

Page: 311

View: 9971

A review of our current understanding of the physical phenomena associated with the flow of blood through the brain, applying these concepts to the physiological and medical aspects of cerebrovascular disease so as to be useful to both the scientist and the clinician. Specifically the book discusses the physical bases for the development of cerebrovascular disease and for its clinical consequences; specific current and possible future therapies; experimental, clinical, and computational techniques used to investigate cerebrovascular disease; blood dynamics and its role; imaging methods used in the diagnosis and management of cerebrovascular disease. Intended as a one- or two-semester course in biophysics, biomedical engineering or medical physics, this is also of interest to medical students and interns in neurology and cardiology, and provides a useful overview of current practice for researchers and clinicians.
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The Boundary Value Problems of Mathematical Physics

Author: O.A. Ladyzhenskaya

Publisher: Springer Science & Business Media

ISBN: 1475743173

Category: Science

Page: 322

View: 4290

In the present edition I have included "Supplements and Problems" located at the end of each chapter. This was done with the aim of illustrating the possibilities of the methods contained in the book, as well as with the desire to make good on what I have attempted to do over the course of many years for my students-to awaken their creativity, providing topics for independent work. The source of my own initial research was the famous two-volume book Methods of Mathematical Physics by D. Hilbert and R. Courant, and a series of original articles and surveys on partial differential equations and their applications to problems in theoretical mechanics and physics. The works of K. o. Friedrichs, which were in keeping with my own perception of the subject, had an especially strong influence on me. I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space. This desire was successfully realized thanks to the introduction of various classes of general solutions and to an elaboration of the methods of proof for the corresponding uniqueness theorems. This was accomplished on the basis of comparatively simple integral inequalities for arbitrary functions and of a priori estimates of the solutions of the problems without enlisting any special representations of those solutions.
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Basic Concepts in Computational Physics

Author: Benjamin A. Stickler,Ewald Schachinger

Publisher: Springer

ISBN: 3319272659

Category: Science

Page: 409

View: 4168

This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.
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Fundamentals of Continuum Mechanics

With Applications to Mechanical, Thermomechanical, and Smart Materials

Author: Stephen Bechtel,Robert Lowe

Publisher: Academic Press

ISBN: 0123948347

Category: Science

Page: 340

View: 1698

Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors’ own research
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Elements of Partial Differential Equations

Author: Pavel Drabek,Gabriela Holubová

Publisher: Walter de Gruyter

ISBN: 9783110191240

Category: Mathematics

Page: 245

View: 3816

This book presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEsand learns some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. An elementary introduction to the basic principles of partial differential equations. With many illustrations.
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Linear Integral Equations

Author: Rainer Kress

Publisher: Springer Science & Business Media

ISBN: 1461495938

Category: Mathematics

Page: 412

View: 5097

This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)
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Partial Differential Equations I

Basic Theory

Author: Michael Eugene Taylor,Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 9780387946535

Category: Mathematics

Page: 563

View: 3164

This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.
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