Partial Differential Equations And Boundary Value Problems With Applications
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Partial Differential Equations And Boundary Value Problems With Applications
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Author : Mark A. Pinsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Partial Differential Equations And Boundary Value Problems With Applications written by Mark A. Pinsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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 And Boundary Value Problems With Applications
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Author : Mark A. Pinsky
language : en
Publisher:
Release Date : 2003
Partial Differential Equations And Boundary Value Problems With Applications written by Mark A. Pinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
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 th.
Partial Differential Equations And Boundary Value Problems With Applications
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Author : Mark A. Pinsky
language : en
Publisher:
Release Date : 2003
Partial Differential Equations And Boundary Value Problems With Applications written by Mark A. Pinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Boundary value problems categories.
Boundary Value Problems For Partial Differential Equations And Applications In Electrodynamics
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Author : N E Toymasyan
language : en
Publisher: World Scientific
Release Date : 1994-02-08
Boundary Value Problems For Partial Differential Equations And Applications In Electrodynamics written by N E Toymasyan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-08 with Mathematics categories.
The book is devoted to boundary value problems for general partial differential equations. Efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions and having great theoretical and practical importance are developed.A new approach to the investigation of electromagnetic fields is sketched, permitting laws of propagation of electromagnetic energy at a great distance, is outlined and asymptotic formulae for solutions of Maxwell's equation is obtained. These equations are also applied to the efficient resolution of problems.The book is based mostly on the investigation of the author, a considerable part of which being published for the first time.
Ordinary And Partial Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-13
Ordinary And Partial Differential Equations written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-13 with Mathematics categories.
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 For Partial Differential Equations And Applications
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Author : Jacques-Louis Lions
language : en
Publisher: Elsevier Masson
Release Date : 1993
Boundary Value Problems For Partial Differential Equations And Applications written by Jacques-Louis Lions and has been published by Elsevier Masson this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Boundary value problems categories.
Applied Differential Equations With Boundary Value Problems
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Author : Vladimir Dobrushkin
language : en
Publisher: CRC Press
Release Date : 2017-10-19
Applied Differential Equations With Boundary Value Problems written by Vladimir Dobrushkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
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.
Unified Transform For Boundary Value Problems
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Author : Athanasios S. Fokas
language : en
Publisher: SIAM
Release Date : 2014-12-30
Unified Transform For Boundary Value Problems written by Athanasios S. Fokas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Partial Differential Equations
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Author : Deborah E. Richards
language : en
Publisher: Nova Science Publishers
Release Date : 2015
Partial Differential Equations written by Deborah E. Richards and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. The authors also investigate nonlinear control problems for couple partial differential equations arising from climate and circulation dynamics in the equatorial zone; the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras; and the existence and properties of solutions, applications in sequential optimal control with pointwise in time state constraints.