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Fourier Analysis And Boundary Value Problems

Author: Enrique A. Gonzalez-Velasco
Publisher: Elsevier
ISBN: 9780080531939
Size: 22.39 MB
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Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field. Topics are covered from a historical perspective with biographical information on key contributors to the field The text contains more than 500 exercises Includes practical applications of the equations to problems in both engineering and physics

Fourier Series Transforms And Boundary Value Problems

Author: J. Ray Hanna
Publisher: Courier Corporation
ISBN: 0486466736
Size: 59.76 MB
Format: PDF, Mobi
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This volume introduces Fourier and transform methods for solutions to boundary value problems associated with natural phenomena. Unlike most treatments, it emphasizes basic concepts and techniques rather than theory. Many of the exercises include solutions, with detailed outlines that make it easy to follow the appropriate sequence of steps. 1990 edition.

Partial Differential Equations With Fourier Series And Boundary Value Problems

Author: Nakhle H. Asmar
Publisher: Courier Dover Publications
ISBN: 0486820831
Size: 17.80 MB
Format: PDF
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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.

Introduction To Partial Differential Equations

Author: Arne Broman
Publisher: Courier Corporation
ISBN: 0486153010
Size: 20.46 MB
Format: PDF, Mobi
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The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. 266 exercises with solutions. 1970 edition.

Fourier Series And Boundary Value Problems

Author: James Ward Brown
Publisher: McGraw-Hill Science, Engineering & Mathematics
Size: 51.44 MB
Format: PDF, Docs
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An introductory treatment of Fourier series and their applications to boundary value problems in partial equations that arise in engineering and physics. This revision incorporates up-to-date mathematics. Many sections have been rewritten to improve the motivation of the theory, and numerous illustrations and exercises have been added throughout the book.

Applied Partial Differential Equations

Author: Richard Haberman
Publisher: Prentice Hall
ISBN: 9780130652430
Size: 73.67 MB
Format: PDF, ePub
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Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linear wave equations and a brief introduction to Laplace transform solution of partial differential equations. For scientists and engineers.

Ordinary And Partial Differential Equations

Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 0387791469
Size: 29.13 MB
Format: PDF, ePub
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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.

Boundary Value Problems

Author: David L. Powers
Publisher: Elsevier
ISBN: 1483269787
Size: 37.29 MB
Format: PDF, Mobi
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Boundary Value Problems is a text material on partial differential equations that teaches solutions of boundary value problems. The book also aims to build up intuition about how the solution of a problem should behave. The text consists of seven chapters. Chapter 1 covers the important topics of Fourier Series and Integrals. The second chapter deals with the heat equation, introducing separation of variables. Material on boundary conditions and Sturm-Liouville systems is included here. Chapter 3 presents the wave equation; estimation of eigenvalues by the Rayleigh quotient is mentioned briefly. The potential equation is the topic of Chapter 4, which closes with a section on classification of partial differential equations. Chapter 5 briefly covers multidimensional problems and special functions. The last two chapters, Laplace Transforms and Numerical Methods, are discussed in detail. The book is intended for third and fourth year physics and engineering students.

Elementary Boundary Value Problems

Author: Theodore A. Bick
Publisher: CRC Press
ISBN: 9780824788995
Size: 60.97 MB
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This textbook elucidates the role of BVPs as models of scientific phenomena, describes traditional methods of solution and summarizes the ideas that come from the solution techniques, centering on the concept of orthonormal sets of functions as generalizations of the trigonometric functions. To reinforce important concepts, the book contains exercises that range in difficulty from routine applications of the material just covered to extensions of that material.;Emphasizing the unifying nature of the material, this book: constructs physical models for both bounded and unbounded domains using rectangular and other co-ordinate systems; develops methods of characteristics, eigenfunction expansions, and transform procedures using the traditional fourier series, D'Alembert's method , and fourier integral transforms; makes explicit connections with linear algebra, analysis, complex variables, set theory, and topology in response to the need to solve BVP's employing Sturm-Liouville ststems as the primary vehicle; and presents illustrative examples in science and engineering, such as versions of the wave, diffusion equations and Laplace's equations.;Providing fundamental definitions for students with no prior experience in this topic other than differential equations, this text is intended as a resource for upper-level undergraduates in mathematics, physics and engineering, and students on courses on boundary value problems.