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A treatise on the calculus of finite differences 有限差分论

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A treatise on the calculus of finite differences 有限差分论

最 低 价:¥386.50

定 价:¥859.00

作 者:GeorgeBoole 著

出 版 社:

出版时间:2003-1-1

I S B N:048649523X

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内容简介

  This is a classic mathematical treatise on the calculus of finite differences. Written by the great English mathematician George Boole, it is a thorough discussion of the basic principles of the subject, covering nearly all the major theorems and methods with clarity and rigor.
  The author begins with a discussion of the differences of elementary functions, explaining and proving such important theorems as Maclaurin's Theorem and Herschel's Theorem. He goes on to treat interpolation, mechanical quadrature, finite integration, and the summation of series, covering such topics as factorials, periodical constants, and the values of Bernoulli's numbers. Several useful tests for the convergence and divergence of series are developed, as is a method for finding the limits of error in series expansions.
  The latter half of the book presents a detailed and thorough discussion of difference-equations. The general theory of difference-equations of the first order is developed completely, and chapters are also included on linear, mixed, and partial difference-equations. The book concludes with applications to problems in geometry and optics.
  One of the most valuable features of the book is the particular attention it pays to the connection of the calculus of finite differences with the differential calculus. Many theorems are expressed in the forms they take in each field, and the student can therefore become acquainted with the close analogy between the two disciplines.
  More than 200 problems are provided to allow the student to test his knowledge of the principles developed in the text. (All problems with numerical solutions are supplied with answers.) There are also scores of numerical examples illustrating basic theorems throughout the book.

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目录

DIFFERENCE-AND SUM-CALCULUS
 CHATPER 1 NATURE OF THE CALCULUS OF FINITE DIFFERENCES
 CHATPER 2 DIRECT THEOREMS OF FINITE DIFFERENCES
 CHATPER 3 ON INTERPOLATION,AND MECHANICAL QUADRATCRE
 CHATPER 4 FINITE INTEGRATION,ADN THE SUMMATION OF SERIES
 CHATPER 5 THE APPROXIMATE SUMMATION OF SERIES
 CHATPER 6 BERNOULLI‘S NUMBERS,AND FACTORIAL COEFFICIENTS
 CHATPER 7 CONVERGENCY AND DIVERGENCY OF SERIES
 CHATPER 8 EXACT THEOREMS
DIFFERENCE-AMD FIMCTOPMA; EQIATOPMS
 CHATPER 9 DIFFERENCE-EQUATIONS OF THE FIRST ORDER
 CHATPER 10 GENERAL THEORY OF THE SOLUTIONS OF DIFFERENCE-AMD DOFFEREMTIAL EQUATIONS OF THE FIRST ORDER
 CHATPER 11 LINEAR DIFFERENCE-EQUATIONS WITH CONSTANT COEFFICIENTS
 CHATPER 12 MISCELLANCOUS PROPOSITIONS AND EQUATIONS SIMULANEOUS EQUATIONS
 CHATPER 13 LINEAR EQUATION WITH VARIABLE COEFFICIENTS SYMBOLICAL AND GENERAL METHODS
 CHATPER 14 MIXED AND PARTIAL DIFFERENCE-EQUATIONS
 CHATPER 15 OF THE CALCULUS OF FUNCTIONS
 CHATPER 16 GEOMETRICAL APPLICATIONS
ANSWERS TO THE EXERCISES

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