Author: C. R. MacCluer
Publisher: Institute of Electrical & Electronics Engineers(IEEE)
ISBN:
Category : Mathematics
Languages : en
Pages : 372
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Book Description
For a first course in the topic using the modern, norm-based Sobolev techniques not currently available in published format. Major concepts are presented with minimal possible detail and details are pushed into the exercises, omitted, or postponed until later sections. Includes worked examples of pr
Author: Charles R. MacCluer
Publisher: Courier Corporation
ISBN: 0486153177
Category : Mathematics
Languages : en
Pages : 382
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Book Description
Based on modern Sobolev methods, this text integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. 2004 edition. Includes 64 figures. Exercises.
Author: Charles R. MacCluer
Publisher: Dover Publications
ISBN: 9780486788678
Category :
Languages : en
Pages : 384
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Book Description
Based on modern Sobolev methods, this text integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. 2004 edition. Includes 64 figures. Exercises.
Author: Vladimir Dobrushkin
Publisher: CRC Press
ISBN: 1498733727
Category : Mathematics
Languages : en
Pages : 1225
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Book Description
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.
Author: Mark McKibben
Publisher: CRC Press
ISBN: 1420092073
Category : Mathematics
Languages : en
Pages : 458
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Book Description
Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging, accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. It gives nonspecialists, even those with minimal prior exposure to analysis, the foundation to understand what evolution equations are and how to work with them in various areas of practice. After presenting the essentials of analysis, the book discusses homogenous finite-dimensional ordinary differential equations. Subsequent chapters then focus on linear homogenous abstract, nonhomogenous linear, semi-linear, functional, Sobolev-type, neutral, delay, and nonlinear evolution equations. The final two chapters explore research topics, including nonlocal evolution equations. For each class of equations, the author develops a core of theoretical results concerning the existence and uniqueness of solutions under various growth and compactness assumptions, continuous dependence upon initial data and parameters, convergence results regarding the initial data, and elementary stability results. By taking an applications-oriented approach, this self-contained, conversational-style book motivates readers to fully grasp the mathematical details of studying evolution equations. It prepares newcomers to successfully navigate further research in the field.
Author: M. Necati Ozisik
Publisher: Courier Corporation
ISBN: 0486782867
Category : Technology & Engineering
Languages : en
Pages : 515
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Book Description
Intended for first-year graduate courses in heat transfer, this volume includes topics relevant to chemical and nuclear engineering and aerospace engineering. The systematic and comprehensive treatment employs modern mathematical methods of solving problems in heat conduction and diffusion. Starting with precise coverage of heat flux as a vector, derivation of the conduction equations, integral-transform technique, and coordinate transformations, the text advances to problem characteristics peculiar to Cartesian, cylindrical, and spherical coordinates; application of Duhamel's method; solution of heat-conduction problems; and the integral method of solution of nonlinear conduction problems. Additional topics include useful transformations in the solution of nonlinear boundary value problems of heat conduction; numerical techniques such as the finite differences and the Monte Carlo method; and anisotropic solids in relation to resistivity and conductivity tensors. Illustrative examples and problems amplify the text, which is supplemented by helpful appendixes.
Author: Mark A. Pinsky
Publisher: American Mathematical Soc.
ISBN: 0821868896
Category : Mathematics
Languages : en
Pages : 545
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Book Description
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.
Author: Allan M. Krall
Publisher: Birkhäuser
ISBN: 303488155X
Category : Mathematics
Languages : en
Pages : 355
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Book Description
The following tract is divided into three parts: Hilbert spaces and their (bounded and unbounded) self-adjoint operators, linear Hamiltonian systemsand their scalar counterparts and their application to orthogonal polynomials. In a sense, this is an updating of E. C. Titchmarsh's classic Eigenfunction Expansions. My interest in these areas began in 1960-61, when, as a graduate student, I was introduced by my advisors E. J. McShane and Marvin Rosenblum to the ideas of Hilbert space. The next year I was given a problem by Marvin Rosenblum that involved a differential operator with an "integral" boundary condition. That same year I attended a class given by the Physics Department in which the lecturer discussed the theory of Schwarz distributions and Titchmarsh's theory of singular Sturm-Liouville boundary value problems. I think a Professor Smith was the in structor, but memory fails. Nonetheless, I am deeply indebted to him, because, as we shall see, these topics are fundamental to what follows. I am also deeply indebted to others. First F. V. Atkinson stands as a giant in the field. W. N. Everitt does likewise. These two were very encouraging to me during my younger (and later) years. They did things "right." It was a revelation to read the book and papers by Professor Atkinson and the many fine fundamen tal papers by Professor Everitt. They are held in highest esteem, and are given profound thanks.
Author: Nakhle H. Asmar
Publisher: Courier Dover Publications
ISBN: 0486820831
Category : Mathematics
Languages : en
Pages : 818
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Book Description
Rich in proofs, examples, and exercises, this widely adopted text emphasizes physics and engineering applications. The Student Solutions Manual can be downloaded free from Dover's site; instructions for obtaining the Instructor Solutions Manual is included in the book. 2004 edition, with minor revisions.
Author: Dennis G. Zill
Publisher: Brooks Cole
ISBN:
Category : Mathematics
Languages : en
Pages : 710
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Book Description
This new Fifth Edition of Zill and Cullen's best-selling book provides a thorough treatment of boundary-value problems and partial differential equations. This edition maintains all the features and qualities that have made Differential Equations with Boundary-Value Problems popular and successful over the years. Written in a straightforward, readable, helpful, not-too-theoretical manner, this new edition keeps the reader firmly in mind and strikes a perfect balance between the teaching of traditional content and the incorporation of evolving technology.
