Applied Differential Equations with Boundary Value Problems


Author: Vladimir Dobrushkin
Publisher: CRC Press
ISBN: 1498733689
Category: Mathematics
Page: 684
View: 5322

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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.

Differential Equations with Boundary-Value Problems


Author: Dennis G. Zill,Warren S Wright
Publisher: Cengage Learning
ISBN: 1111827060
Category: Mathematics
Page: 664
View: 4773

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DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 8th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, the book provides a thorough treatment of 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.

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (Classic Version)


Author: Richard Haberman
Publisher: Pearson
ISBN: 9780134995434
Category: Boundary value problems
Page: 784
View: 1752

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This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green's functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics.

Introductory Differential Equations

with Boundary Value Problems, Student Solutions Manual (e-only)
Author: Martha L. Abell,James P. Braselton
Publisher: Academic Press
ISBN: 9780123846655
Category: Mathematics
Page: 212
View: 2059

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This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging. Many different majors will require differential equations and applied mathematics, so there should be a lot of interest in an intro-level text like this. The accessible writing style will be good for non-math students, as well as for undergrad classes.

Applied Partial Differential Equations


Author: J. David Logan
Publisher: Springer Science & Business Media
ISBN: 9780387209357
Category: Mathematics
Page: 209
View: 1438

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"This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation, epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced."--BOOK JACKET.

Boundary Value Problems of Mathematical Physics

2-Volume Set
Author: Ivar Stakgold
Publisher: SIAM
ISBN: 1611972388
Category:
Page: 748
View: 6934

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For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.

Partial Differential Equations and Boundary Value Problems with Maple


Author: George A. Articolo
Publisher: Academic Press
ISBN: 0080885063
Category: Mathematics
Page: 744
View: 5078

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Partial Differential Equations and Boundary Value Problems with Maple, Second Edition, presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours - an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. This updated edition provides a quick overview of the software w/simple commands needed to get started. It includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations. It also incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions. Numerous example problems and end of each chapter exercises are provided. Provides a quick overview of the software w/simple commands needed to get started Includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations Incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions Numerous example problems and end of each chapter exercises

A Course in Differential Equations with Boundary Value Problems


Author: Stephen A. Wirkus,Randall J. Swift,Ryan Szypowski
Publisher: CRC Press
ISBN: 1498736068
Category: Mathematics
Page: 768
View: 9852

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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

A Course in Differential Equations with Boundary Value Problems, Second Edition


Author: Stephen A. Wirkus,Randall J. Swift,Ryan Szypowski
Publisher: CRC Press
ISBN: 1498736084
Category: Mathematics
Page: 788
View: 2573

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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

Partial Integral Operators and Integro-Differential Equations

Pure and Applied Mathematics
Author: Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko
Publisher: CRC Press
ISBN: 9780824703967
Category: Mathematics
Page: 578
View: 823

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A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.

Boundary Value Problems

And Partial Differential Equations
Author: David L. Powers
Publisher: Academic Press
ISBN: 0125637381
Category: Mathematics
Page: 501
View: 4434

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Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering. * CD with animations and graphics of solutions, additional exercises and chapter review questions * Nearly 900 exercises ranging in difficulty * Many fully worked examples

Problems in Applied Mathematics


Author: Murray S. Klamkin
Publisher: SIAM
ISBN: 0898712599
Category: Mathematics
Page: 588
View: 8312

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A compilation of 380 of SIAM Review's most interesting problems dating back to the journal's inception in 1959.

Partial Differential Equations and Boundary-value Problems with Applications


Author: Mark A. Pinsky
Publisher: American Mathematical Soc.
ISBN: 0821868896
Category: Mathematics
Page: 526
View: 4738

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Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

Partial Differential Equations with Fourier Series and Boundary Value Problems

Third Edition
Author: Nakhle H. Asmar
Publisher: Courier Dover Publications
ISBN: 0486820831
Category: Mathematics
Page: 816
View: 7886

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This text provides an introduction to partial differential equations and boundary value problems, including Fourier series. The treatment offers students a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential equations. This widely adopted and successful book also serves as a valuable reference for engineers and other professionals. The approach emphasizes applications, with particular stress on physics and engineering applications. Rich in proofs and examples, the treatment features many exercises in each section. Relevant Mathematica files are available for download from author Nakhlé Asmar's website; however, the book is completely usable without computer access. The Students' Solutions Manual can be downloaded for free from the Dover website, and the Instructor's Solutions Manual is available upon request for professors and potential teachers. The text is suitable for undergraduates in mathematics, physics, engineering, and other fields who have completed a course in ordinary differential equations.

Green's Functions and Boundary Value Problems


Author: Ivar Stakgold,Michael J. Holst
Publisher: John Wiley & Sons
ISBN: 0470906529
Category: Mathematics
Page: 736
View: 8754

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Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.

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: 3027

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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.

Partial Differential Equations and Boundary Value Problems


Author: Viorel Barbu
Publisher: Springer Science & Business Media
ISBN: 9401591172
Category: Mathematics
Page: 284
View: 7608

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The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of the Romanian Academy. The book focuses on classical boundary value problems for the principal equations of mathematical physics: second order elliptic equations (the Poisson equations), heat equations and wave equations. The existence theory of second order elliptic boundary value problems was a great challenge for nineteenth century mathematics and its development was marked by two decisive steps. Undoubtedly, the first one was the Fredholm proof in 1900 of the existence of solutions to Dirichlet and Neumann problems, which represented a triumph of the classical theory of partial differential equations. The second step is due to S. 1. Sobolev (1937) who introduced the concept of weak solution in partial differential equations and inaugurated the modern theory of boundary value problems. The classical theory which is a product ofthe nineteenth century, is concerned with smooth (continuously differentiable) sollutions and its methods rely on classical analysis and in particular on potential theory. The modern theory concerns distributional (weak) solutions and relies on analysis of Sob ole v spaces and functional methods. The same distinction is valid for the boundary value problems associated with heat and wave equations. Both aspects of the theory are present in this book though it is not exhaustive in any sense.

Partial Differential Equations in Mechanics 1

Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation
Author: A.P.S. Selvadurai
Publisher: Springer Science & Business Media
ISBN: 3662040069
Category: Technology & Engineering
Page: 596
View: 2029

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This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

Partial Differential Equations & Boundary Value Problems with Maple V


Author: George A. Articolo
Publisher: Academic Press
ISBN: 9780120644759
Category: Mathematics
Page: 628
View: 5545

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George Articulo covers all the material found in traditional partial differentiation equations and boundary value courses in this textbook. Its unique approach allows students to learn the mathematics first, then use Maple graphics capabilities to visualize both static and animated behavior of the solution. The book provides many example problems using commands that render two- or three-dimensional animated graphics. The author focuses on the natural union between partial differential equations and a powerful computational language such as Maple. Assumes no previous experience with Maple V; provides a quick review of the language with some simple commands needed to get started and a quick review of linear algebra Includes a review material in linear algebra and ordinary differential equations, and their contribution in solving partial differential equations Includes an early introduction to Sturm-Liouille boundary problems and generalized eigenfuction expansions Numerous example problems in both one and two spatial dimensions, in both the rectangular and cylindrical coordinate systems; an abundant array of exercises problems at the end of each chapter

Differential Equations

Theory, Technique and Practice, Second Edition
Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 1482247046
Category: Mathematics
Page: 557
View: 7882

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"Krantz is a very prolific writer. He ... creates excellent examples and problem sets." —Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA Designed for a one- or two-semester undergraduate course, Differential Equations: Theory, Technique and Practice, Second Edition educates a new generation of mathematical scientists and engineers on differential equations. This edition continues to emphasize examples and mathematical modeling as well as promote analytical thinking to help students in future studies. New to the Second Edition Improved exercise sets and examples Reorganized material on numerical techniques Enriched presentation of predator-prey problems Updated material on nonlinear differential equations and dynamical systems A new appendix that reviews linear algebra In each chapter, lively historical notes and mathematical nuggets enhance students’ reading experience by offering perspectives on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight rich applications from engineering, physics, and applied science. Problems for review and discovery also give students some open-ended material for exploration and further learning.