## A Treatise on the Calculus of Finite DifferencesThis 1860 classic, written by one of the great mathematicians of the 19th century, was designed as a sequel to his Treatise on Differential Equations (1859). Divided into two sections ("Difference- and Sum-Calculus" and "Difference- and Functional Equations"), and containing more than 200 exercises (complete with answers), Boole discusses: . nature of the calculus of finite differences . direct theorems of finite differences . finite integration, and the summation of series . Bernoulli's number, and factorial coefficients . convergency and divergency of series . difference-equations of the first order . linear difference-equations with constant coefficients . mixed and partial difference-equations . and much more. No serious mathematician's library is complete without A Treatise on the Calculus of Finite Differences. English mathematician and logician GEORGE BOOLE (1814-1864) is best known as the founder of modern symbolic logic, and as the inventor of Boolean algebra, the foundation of the modern field of computer science. His other books include An Investigation of the Laws of Thought (1854). |

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absolute constant algebraical analogous apply approximate value arbitrary constant assume becomes Bernoulli's numbers binomial Calculus of Finite CHAPTER complete primitive condition convergent series corresponding Crelle curve deduce Definite Integrals degree denoted derived determine developed Differential Calculus differential coefficients differential equation divergent series equa equal example expansion expression factor find the sum Finite Differences formula fraction functional equation geometrical series given equation gives Hence indefinitely increased independent variable indirect integral infinite Infinitesimal Calculus integral function interpolation involving Lagrange's Lagrange's formula linear difference-equation linear equation method notation obtain operation particular integral particular value performing periodical function point-systems rational and integral reduced represented result roots satisfied second member Shew shewn singular solution Solve the equation substituting successive differences successive values summation supposed Taylor's Theorem theorem tion vanish whence

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Page 9 - Jacobi polynomials will be found in the exercises at the end of this chapter.