Elementary Fluid Dynamics

Author: D. J. Acheson

Publisher: Oxford University Press

ISBN: 0198596790

Category: Mathematics

Page: 397

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This textbook provides a clear and concise introduction to both theory and application of fluid dynamics, suitable for all undergraduates coming to the subject for the first time. It has a wide scope, with frequent references to experiments, and numerous exercises illustrating the main ideas.

Numerical Solution of Partial Differential Equations

Finite Difference Methods

Author: Gordon D. Smith

Publisher: Oxford University Press

ISBN: 9780198596509

Category: Mathematics

Page: 337

View: 5794

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Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Applied Partial Differential Equations

Author: J. R. Ockendon,Sam Howison,Andrew Lacey,Alexander Movchan

Publisher: Oxford University Press on Demand

ISBN: 9780198527718

Category: Mathematics

Page: 449

View: 7941

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Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This revised edition of Applied Partial Differential Equations contains many new sections and exercises including transform methods, free surface flows, linear elasticity and complex characteristics.

The Finite Element Method

An Introduction with Partial Differential Equations

Author: A. J. Davies

Publisher: Oxford University Press

ISBN: 0199609136

Category: Mathematics

Page: 297

View: 3729

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An introduction to the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. Contains worked examples throughout and each chapter has a set of exercises with detailed solutions.

An Introduction to Partial Differential Equations

Author: Yehuda Pinchover,Jacob Rubinstein

Publisher: Cambridge University Press

ISBN: 1139444913

Category: Mathematics

Page: N.A

View: 9927

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A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green's functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples. Solutions to selected exercises are included for students whilst extended solution sets are available to lecturers from [email protected]

Numerical Solution of Partial Differential Equations

Finite Difference Methods

Author: Gordon D. Smith

Publisher: Oxford University Press

ISBN: 9780198596509

Category: Mathematics

Page: 337

View: 2526

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Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Partial Differential Equations of Applied Mathematics

Author: Erich Zauderer

Publisher: Wiley-Interscience

ISBN: 9780471315162

Category: Mathematics

Page: 894

View: 7830

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The only comprehensive guide to modeling, characterizing, and solving partial differential equations This classic text by Erich Zauderer provides a comprehensive account of partial differential equations and their applications. Dr. Zauderer develops mathematical models that give rise to partial differential equations and describes classical and modern solution techniques. With an emphasis on practical applications, he makes liberal use of real-world examples, explores both linear and nonlinear problems, and provides approximate as well as exact solutions. He also describes approximation methods for simplifying complicated solutions and for solving linear and nonlinear problems not readily solved by standard methods. The book begins with a demonstration of how the three basic types of equations (parabolic, hyperbolic, and elliptic) can be derived from random walk models. It continues in a less statistical vein to cover an exceptionally broad range of topics, including stabilities, singularities, transform methods, the use of Green's functions, and perturbation and asymptotic treatments. Features that set Partial Differential Equations of Applied Mathematics, Second Edition above all other texts in the field include: Coverage of random walk problems, discontinuous and singular solutions, and perturbation and asymptotic methods More than 800 practice exercises, many of which are fully worked out Numerous up-to-date examples from engineering and the physical sciences Partial Differential Equations of Applied Mathematics, Second Edition is a superior advanced-undergraduate to graduate-level text for students in engineering, the sciences, and applied mathematics. The title is also a valuable working resource for professionals in these fields. Dr. Zauderer received his doctorate in mathematics from the New York University-Courant Institute. Prior to joining the staff of Polytechnic University, he was a Senior Weitzmann Fellow of the Weitzmann Institute of Science in Rehovot, Israel.

Function Spaces and Partial Differential Equations

Author: Ali Taheri

Publisher: Oxford University Press, USA

ISBN: 0198733135

Category: Differential equations, Partial

Page: 528

View: 1592

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This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Numerical Data Fitting in Dynamical Systems

A Practical Introduction with Applications and Software

Author: Klaus Schittkowski

Publisher: Springer Science & Business Media

ISBN: 1441957626

Category: Computers

Page: 396

View: 4787

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Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.

Partial Differential Equations

Analytical and Numerical Methods, Second Edition

Author: Mark S. Gockenbach

Publisher: SIAM

ISBN: 0898719356

Category: Mathematics

Page: 654

View: 2707

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A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.

Nonlinear Ordinary Differential Equations

An Introduction to Dynamical Systems

Author: Dominic William Jordan,Peter Smith

Publisher: Oxford University Press, USA

ISBN: 9780198565628

Category: Mathematics

Page: 550

View: 1842

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The text of this edition has been revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. It is directed towards practical applications of the theory with examples and problems.

Partial differential equations in general relativity

Author: Alan D. Rendall

Publisher: Oxford University Press, USA

ISBN: 9780199215409

Category: Mathematics

Page: 279

View: 1332

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A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology.

Theory and Computation of Hydrodynamic Stability

Author: W. O. Criminale,T. L. Jackson,Ronald Douglas Joslin

Publisher: Cambridge University Press

ISBN: 9780521632003

Category: Mathematics

Page: 441

View: 5428

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Graduate text/reference with exercises, computer code on basic topic in fluid dynamics.

Numerical Mathematics

Author: Alfio Quarteroni,Riccardo Sacco,Fausto Saleri

Publisher: Springer Science & Business Media

ISBN: 3540498095

Category: Mathematics

Page: 657

View: 6504

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This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been

Numerical Methods for Delay Differential Equations

Author: Alfredo Bellen,Marino Zennaro

Publisher: Oxford University Press

ISBN: 0198506546

Category: Business & Economics

Page: 395

View: 732

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This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.

Partial Differential Equations of Applied Mathematics

Author: Erich Zauderer

Publisher: John Wiley & Sons

ISBN: 1118031407

Category: Mathematics

Page: 968

View: 5203

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This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.