Modern Methods in Partial Differential Equations

Author: Martin Schechter

Publisher: Courier Corporation

ISBN: 0486492966

Category: Mathematics

Page: 256

View: 990

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When first published in 1977, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Now it remains a permanent, much-cited contribution to the ever-expanding literature.

Hilbert Space Methods in Partial Differential Equations

Author: Ralph E. Showalter

Publisher: Courier Corporation

ISBN: 0486135799

Category: Mathematics

Page: 224

View: 7516

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This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Abstract Methods in Partial Differential Equations

Author: Robert W. Carroll,Mathematics

Publisher: Courier Corporation

ISBN: 0486488357

Category: Mathematics

Page: 374

View: 1864

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This self-contained text is directed to graduate students with some previous exposure to classical partial differential equations. Readers can attain a quick familiarity with various abstract points of view in partial differential equations, allowing them to read the literature and begin thesis work. The author's detailed presentation requires no prior knowledge of many mathematical subjects and illustrates the methods' applicability to the solution of interesting differential problems. The treatment emphasizes existence-uniqueness theory as a topic in functional analysis and examines abstract evolution equations and ordinary differential equations with operator coefficients. A concluding chapter on global analysis develops some basic geometrical ideas essential to index theory, overdetermined systems, and related areas. In addition to exercises for self-study, the text features a thorough bibliography. Appendixes cover topology and fixed-point theory in addition to Banach algebras, analytic functional calculus, fractional powers of operators, and interpolation theory.

Ordinary Differential Equations

An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences

Author: Morris Tenenbaum,Harry Pollard

Publisher: Courier Corporation

ISBN: 0486649407

Category: Mathematics

Page: 808

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Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Author: Claes Johnson

Publisher: Courier Corporation

ISBN: 0486131599

Category: Mathematics

Page: 288

View: 9160

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An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Basic Linear Partial Differential Equations

Author: Francois Treves

Publisher: Courier Corporation

ISBN: 0486150984

Category: Mathematics

Page: 496

View: 7716

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Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students employs nontraditional methods to explain classical material. Nearly 400 exercises. 1975 edition.

Introduction to Partial Differential Equations with Applications

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

Publisher: Courier Corporation

ISBN: 048613217X

Category: Mathematics

Page: 432

View: 7184

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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.

Lectures on Partial Differential Equations

Author: I. G. Petrovsky

Publisher: Courier Corporation

ISBN: 0486155080

Category: Mathematics

Page: 272

View: 7959

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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.

Introduction to Partial Differential Equations

Author: Donald Greenspan

Publisher: Courier Corporation

ISBN: 0486150933

Category: Mathematics

Page: 204

View: 3069

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Designed for use in a 1-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, 2nd-order partial differential equations, wave equation, potential equation, heat equation, and more. Includes exercises. 1961 edition.

Partial differential equations

an introduction

Author: David L. Colton

Publisher: Dover Pubns

ISBN: N.A

Category: Mathematics

Page: 308

View: 1620

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This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. Includes examples of inverse problems arising from improperly posed applications as well as exercises, many with answers. 1988 edition.

Numerical Methods for Partial Differential Equations

Author: G. Evans,J. Blackledge,P. Yardley

Publisher: Springer Science & Business Media

ISBN: 1447103777

Category: Mathematics

Page: 290

View: 9584

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The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. James Clerk Maxwell, for example, put electricity and magnetism into a unified theory by establishing Maxwell's equations for electromagnetic theory, which gave solutions for prob lems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechanical processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forecasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.

Partial Differential Equations of Mathematical Physics

Author: S. L. Sobolev

Publisher: Courier Corporation

ISBN: 9780486659640

Category: Science

Page: 427

View: 8473

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This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.

Elements of Partial Differential Equations

Author: Ian N. Sneddon

Publisher: Courier Corporation

ISBN: 0486452972

Category: Mathematics

Page: 327

View: 3438

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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 of Mathematical Physics

Second Edition

Author: Arthur Godon Webster

Publisher: Courier Dover Publications

ISBN: 0486805158

Category: Mathematics

Page: 464

View: 4780

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A classic treatise on partial differential equations, this comprehensive work by one of America's greatest early mathematical physicists covers the basic method, theory, and application of partial differential equations. In addition to its value as an introductory and supplementary text for students, this volume constitutes a fine reference for mathematicians, physicists, and research engineers. Detailed coverage includes Fourier series; integral and elliptic equations; spherical, cylindrical, and ellipsoidal harmonics; Cauchy's method; boundary problems; the Riemann-Volterra method; and many other basic topics. The self-contained treatment fully develops the theory and application of partial differential equations to virtually every relevant field: vibration, elasticity, potential theory, the theory of sound, wave propagation, heat conduction, and many more. A helpful Appendix provides background on Jacobians, double limits, uniform convergence, definite integrals, complex variables, and linear differential equations.

A First Course in Partial Differential Equations

with Complex Variables and Transform Methods

Author: H. F. Weinberger

Publisher: Courier Corporation

ISBN: 0486132048

Category: Mathematics

Page: 480

View: 1495

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Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.

Solution Techniques for Elementary Partial Differential Equations, Third Edition

Author: Christian Constanda

Publisher: CRC Press

ISBN: 1498704964

Category: Mathematics

Page: 358

View: 2243

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Solution Techniques for Elementary Partial Differential Equations, Third Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). Making the text even more user-friendly, this third edition covers important and widely used methods for solving PDEs. New to the Third Edition New sections on the series expansion of more general functions, other problems of general second-order linear equations, vibrating string with other types of boundary conditions, and equilibrium temperature in an infinite strip Reorganized sections that make it easier for students and professors to navigate the contents Rearranged exercises that are now at the end of each section/subsection instead of at the end of the chapter New and improved exercises and worked examples A brief Mathematica® program for nearly all of the worked examples, showing students how to verify results by computer This bestselling, highly praised textbook uses a streamlined, direct approach to develop students’ competence in solving PDEs. It offers concise, easily understood explanations and worked examples that allow students to see the techniques in action.

Partial Differential Equations of Applied Mathematics

Author: Erich Zauderer

Publisher: Wiley-Interscience

ISBN: 9780471315162

Category: Mathematics

Page: 894

View: 515

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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.

Partial Differential Equations for Scientists and Engineers

Author: Stanley J. Farlow

Publisher: Courier Corporation

ISBN: 0486134733

Category: Mathematics

Page: 414

View: 4141

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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.

Partial Differential Equations of Mathematical Physics and Integral Equations

Author: Ronald B. Guenther,John W. Lee

Publisher: Courier Corporation

ISBN: 0486137627

Category: Mathematics

Page: 576

View: 1623

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Superb treatment for math and physical science students discusses modern mathematical techniques for setting up and analyzing problems. Discusses partial differential equations of the 1st order, elementary modeling, potential theory, parabolic equations, more. 1988 edition.

Numerical Methods for Scientists and Engineers

Author: Richard Hamming

Publisher: Courier Corporation

ISBN: 0486134822

Category: Mathematics

Page: 752

View: 8108

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This inexpensive paperback edition of a groundbreaking text stresses frequency approach in coverage of algorithms, polynomial approximation, Fourier approximation, exponential approximation, and other topics. Revised and enlarged 2nd edition.