Finite Difference Equations

Author: Hyman Levy,F. Lessman

Publisher: Courier Corporation

ISBN: 0486672603

Category: Mathematics

Page: 278

View: 6043

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Comprehensive study focuses on use of calculus of finite differences as an approximation method for solving troublesome differential equations. Elementary difference operations; interpolation and extrapolation; modes of expansion of the solutions of nonlinear equations, applications of difference equations, difference equations associated with functions of two variables, more. Exercises with answers. 1961 edition.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Author: Claes Johnson

Publisher: Courier Corporation

ISBN: 0486131599

Category: Mathematics

Page: 288

View: 4526

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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.

Introduction to Difference Equations

With Illustrative Examples from Economics, Psychology, and Sociology

Author: Samuel Goldberg

Publisher: Courier Corporation

ISBN: 0486650847

Category: Mathematics

Page: 260

View: 8102

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Exceptionally clear exposition of an important mathematical discipline and its applications to sociology, economics, and psychology. Topics include calculus of finite differences, difference equations, matrix methods, and more. 1958 edition.

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

View: 416

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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.

Finite Difference Methods for Ordinary and Partial Differential Equations

Steady-State and Time-Dependent Problems

Author: Randall J. LeVeque

Publisher: SIAM

ISBN: 9780898717839

Category: Differential equations

Page: 339

View: 1466

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This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Introduction to Partial Differential Equations

Author: Donald Greenspan

Publisher: Courier Corporation

ISBN: 9780486414508

Category: Mathematics

Page: 195

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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.

Basic Linear Partial Differential Equations

Author: Francois Treves

Publisher: Courier Corporation

ISBN: 0486150984

Category: Mathematics

Page: 496

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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.

Numerical Solution of Differential Equations

Author: Zhilin Li,Zhonghua Qiao,Tao Tang

Publisher: Cambridge University Press

ISBN: 1107163226

Category: Mathematics

Page: 293

View: 8290

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A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.

An Introduction to the Mathematical Theory of Finite Elements

Author: J. T. Oden,J. N. Reddy

Publisher: Courier Corporation

ISBN: 0486142213

Category: Technology & Engineering

Page: 448

View: 508

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This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.

Introduction to Partial Differential Equations with Applications

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

Publisher: Courier Corporation

ISBN: 048613217X

Category: Mathematics

Page: 432

View: 4845

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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.

Applied Partial Differential Equations

Author: Paul DuChateau,David Zachmann

Publisher: Courier Corporation

ISBN: 048614187X

Category: Mathematics

Page: 640

View: 2510

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DIVBook focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included. /div

Modern Methods in Partial Differential Equations

Author: Martin Schechter

Publisher: Courier Corporation

ISBN: 0486492966

Category: Mathematics

Page: 256

View: 7565

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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.

Stability Theory of Differential Equations

Author: Richard Bellman

Publisher: Courier Corporation

ISBN: 0486150135

Category: Mathematics

Page: 176

View: 8187

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Suitable for advanced undergraduates and graduate students, this text introduces the stability theory and asymptotic behavior of solutions of linear and nonlinear differential equations. 1953 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: 9762

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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.

Generalized Functions and Partial Differential Equations

Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 9780486152912

Category: Mathematics

Page: 352

View: 8400

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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.

Partial Differential Equations with Numerical Methods

Author: Stig Larsson,Vidar Thomee

Publisher: Springer Science & Business Media

ISBN: 3540887059

Category: Mathematics

Page: 262

View: 5531

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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.

Elements of Partial Differential Equations

Author: Ian N. Sneddon

Publisher: Courier Corporation

ISBN: 0486162990

Category: Mathematics

Page: 352

View: 7112

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This text features numerous worked examples in its presentation of elements from the theory of partial differential equations, emphasizing forms suitable for solving equations. Solutions to odd-numbered problems appear at the end. 1957 edition.

Ordinary Differential Equations

Author: Edward L. Ince

Publisher: Courier Corporation

ISBN: 0486158217

Category: Mathematics

Page: 576

View: 6510

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Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.

Lectures on Ordinary Differential Equations

Author: Witold Hurewicz

Publisher: Courier Corporation

ISBN: 048679721X

Category: Mathematics

Page: 144

View: 9342

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Introductory treatment explores existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. "A rigorous and lively introduction." — The American Mathematical Monthly. 1958 edition.