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.

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Bibliographic Details

Title: Finite Difference Equations
Publisher: Dover Publications Inc.
Publication Date: 1992
Language: English
ISBN 10: 0486672603
ISBN 13: 9780486672601
Binding: Paperback
Condition: Good

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Synopsis

The calculus of finite differences is an area of mathematics important to a broad range of professions, from physical science and engineering to social sciences and statistics. This comprehensive study, directed to advanced undergraduate-level students, graduate students, and professionals, concentrates primarily on how the calculus of finite differences may be used as an approximation method for solving troublesome differential equations.
Stressing problem solving rather than pure mathematics, the authors begin with elementary difference operations, treat interpolation and extrapolation, the derivation of difference equations, solution of linear difference equations with variable and constant coefficients, and the properties of the general difference equations. Chapter 5 develops the various modes of expansion of the solutions of nonlinear equations and the conditions under which these are valid. In addition, in Chapter 6, there is the estimation of the eigenvalues that arise in connection with linear difference equations, and the investigation of the properties of the corresponding orthogonal functions in the form of factorial series. The final two chapters treat applications of difference equations, and the investigation of the properties of the corresponding orthogonal functions in the form of factorial series. The final two chapters treat applications of difference equations and difference equations associated with functions of two variables. Included are a number of exercises with answers.

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