A treatise on the calculus of finite differences
著者
書誌事項
A treatise on the calculus of finite differences
（Cambridge library collection, . Mathematical sciences）
Cambridge University Press, 2009
- : pbk
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注記
Reprint. Originally published: Cambridge : Macmillan, 1860
内容説明・目次
内容説明
Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published A Treatise on the Calculus of Finite Differences in 1860 as a sequel to his Treatise on Differential Equations (1859). Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations of partial and mixed differences. Boole also includes exercises for daring students to ponder, and also supplies answers. Long a proponent of positioning logic firmly in the camp of mathematics rather than philosophy, Boole was instrumental in developing a notational system that allowed logical statements to be symbolically represented by algebraic equations. One of history's most insightful mathematicians, Boole is compelling reading for today's student of logic and Boolean thinking.
目次
- Preface to the first edition
- Preface to the second edition
- 1. Nature of the calculus of finite differences
- 2. Direct theorems of finite differences
- 3. On interpolation, and mechanical quadrature
- 4. Finite integration, and the summation of series
- 5. The approximate summation of series
- 6. Bernoulli's numbers, and factorial coefficients
- 7. Convergency and divergency of series
- 8. Exact theorems
- 9. Difference-equations of the first order
- 10. General theory of the solutions of difference- and differential equations of the first order
- 11. Linear difference-equations with constant coefficients
- 12. Miscellaneous propositions and equations. Simultaneous equations
- 13. Linear equations with variable coefficients. Symbolical and general methods
- 14. Mixed and partial difference-equations
- 15. Of the calculus of functions
- 16. Geometrical applications
- Answers to the exercises.
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