Partial Differential Equations of Parabolic Type

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Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 0486318265

Category: Mathematics

Page: 368

View: 2881

With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

Generalized Functions and Partial Differential Equations

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Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 9780486152912

Category: Mathematics

Page: 352

View: 1905

This self-contained text details developments in the theory of generalized functions and the theory of distributions, and it systematically applies them to a variety of problems in partial differential equations. 1963 edition.

Linear and Quasi-linear Equations of Parabolic Type

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Author: Olʹga Aleksandrovna Ladyzhenskai͡a,Vsevolod Alekseevich Solonnikov,Nina N. Ural'tseva

Publisher: American Mathematical Soc.

ISBN: 9780821886533

Category: Mathematics

Page: 648

View: 4243

Lectures on Partial Differential Equations

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Author: I. G. Petrovsky

Publisher: Courier Corporation

ISBN: 0486155080

Category: Mathematics

Page: 272

View: 4284

Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.

Equations of Mathematical Physics

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Author: A. N. Tikhonov,A. A. Samarskii

Publisher: Courier Corporation

ISBN: 0486173364

Category: Science

Page: 800

View: 2268

DIVThorough, rigorous advanced-undergraduate to graduate-level treatment of problems leading to partial differential equations. Hyperbolic, parabolic, elliptic equations; wave propagation in space, heat conduction in space, more. Problems. Appendixes. /div

Introduction to Partial Differential Equations with Applications

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Author: E. C. Zachmanoglou,Dale W. Thoe

Publisher: Courier Corporation

ISBN: 048613217X

Category: Mathematics

Page: 432

View: 8705

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

A Collection of Problems in Mathematical Physics

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Author: Boris Mikha?lovich Budak,Aleksandr Andreevich Samarski?,Andre? Nikolaevich Tikhonov

Publisher: Courier Corporation

ISBN: 0486658066

Category: Science

Page: 768

View: 9105

Outstanding, wide-ranging material on classification and reduction to canonical form of second-order differential equations; hyperbolic, parabolic, elliptic equations, more. Bibliography.

Partial Differential Equations

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Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 048615159X

Category: Mathematics

Page: 272

View: 2511

Largely self-contained, this three-part treatment focuses on elliptic and evolution equations, concluding with a series of independent topics directly related to the methods and results of the preceding sections. 1969 edition.

Hyperbolic Partial Differential Equations

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Author: Peter D. Lax

Publisher: American Mathematical Soc.

ISBN: 0821835769

Category: Mathematics

Page: 217

View: 1157

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses.

Stochastic Differential Equations and Applications

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Author: Avner Friedman

Publisher: Academic Press

ISBN: 1483217876

Category: Mathematics

Page: 248

View: 4741

Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.

Partial Differential Equations of Applied Mathematics

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Author: Erich Zauderer

Publisher: Wiley-Interscience

ISBN: 9780471315162

Category: Mathematics

Page: 894

View: 4047

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.

Stochastic Integration and Differential Equations

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Author: Philip E. Protter

Publisher: Springer

ISBN: 3662100614

Category: Mathematics

Page: 415

View: 8227

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.

Introduction to Partial Differential Equations

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Author: Donald Greenspan

Publisher: Courier Corporation

ISBN: 9780486414508

Category: Mathematics

Page: 195

View: 3209

Rigorous presentation, designed for use in a 1-semester course, explores basics; Fourier series; 2nd-order partial differential equations; wave, potential, and heat equations; approximate solution of partial differential equations, more. Exercises. 1961 edition.

Numerical Solution of Partial Differential Equations in Science and Engineering

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Author: Leon Lapidus,George F. Pinder

Publisher: John Wiley & Sons

ISBN: 1118031210

Category: Mathematics

Page: 677

View: 6500

From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [It] is unique in that it covers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic) mode of presentation. Many different computational schemes are described in great detail . . . Numerous practical examples and applications are described from beginning to the end, often with calculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages to lucid developments of the methods [for solving partial differential equations] . . . the writing is very polished and I found it a pleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen and Eli L. Isaacson. A modern, practical look at numerical analysis, this book guides readers through a broad selection of numerical methods, implementation, and basic theoretical results, with an emphasis on methods used in scientific computation involving differential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan. Presenting an easily accessible treatment of mathematical methods for scientists and engineers, this acclaimed work covers fluid mechanics and calculus of variations as well as more modern methods-dimensional analysis and scaling, nonlinear wave propagation, bifurcation, and singular perturbation. 1996 (0-471-16513-1) 496 pp.

Handbook of Linear Partial Differential Equations for Engineers and Scientists, Second Edition

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Author: Andrei D. Polyanin,Vladimir E. Nazaikinskii

Publisher: CRC Press

ISBN: 1466581492

Category: Mathematics

Page: 1609

View: 7287

Includes nearly 4,000 linear partial differential equations (PDEs) with solutions Presents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fields Outlines basic methods for solving various problems in science and engineering Contains much more linear equations, problems, and solutions than any other book currently available Provides a database of test problems for numerical and approximate analytical methods for solving linear PDEs and systems of coupled PDEs New to the Second Edition More than 700 pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutions Systems of coupled PDEs with solutions Some analytical methods, including decomposition methods and their applications Symbolic and numerical methods for solving linear PDEs with Maple, Mathematica, and MATLAB® Many new problems, illustrative examples, tables, and figures To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity.

Partial Differential Equations with Numerical Methods

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Author: Stig Larsson,Vidar Thomee

Publisher: Springer Science & Business Media

ISBN: 3540887059

Category: Mathematics

Page: 262

View: 1928

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Computational Partial Differential Equations Using MATLAB

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Author: Jichun Li,Yi-Tung Chen

Publisher: CRC Press

ISBN: 9781420089059

Category: Mathematics

Page: 378

View: 4824

This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical methods, such as the high-order compact difference method and the radial basis function meshless method. Helps Students Better Understand Numerical Methods through Use of MATLAB® The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions. All the Material Needed for a Numerical Analysis Course Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.

Elements of Partial Differential Equations

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Author: Ian N. Sneddon

Publisher: Courier Corporation

ISBN: 0486452972

Category: Mathematics

Page: 327

View: 5422

Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory. Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent study will particularly appreciate the worked examples that appear throughout the text.

Partial Differential Equations for Scientists and Engineers

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Author: Stanley J. Farlow

Publisher: Courier Corporation

ISBN: 0486134733

Category: Mathematics

Page: 414

View: 1968

Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.

Introduction to Partial Differential Equations and Hilbert Space Methods

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Author: Karl E. Gustafson

Publisher: Courier Corporation

ISBN: 9780486612713

Category: Mathematics

Page: 448

View: 8731

This volume offers an excellent undergraduate-level introduction to the main topics, methods, and applications of partial differential equations. Chapter 1 presents a full introduction to partial differential equations and Fourier series as related to applied mathematics. Chapter 2 begins with a more comprehensive look at the principal method for solving partial differential equations — the separation of variables — and then more fully develops that approach in the contexts of Hilbert space and numerical methods. Chapter 3 includes an expanded treatment of first-order systems, a short introduction to computational methods, and aspects of topical research on the partial differential equations of fluid dynamics. With over 600 problems and exercises, along with explanations, examples, and a comprehensive section of answers, hints, and solutions, this superb, easy-to-use text is ideal for a one-semester or full-year course. It will also provide the mathematically inclined layperson with a stimulating review of the subject's essentials.