A Treatise on Differential Equations, Opseg 1

Naslovnica
Macmillan, 1859 - Broj stranica: 494
There is an aspect of Boole's work that is not closely related to his treatises in logic or the theory of sets but which is familiar to every student of differential equations. This is the algorithm of differential operators, which he introduced to facilitate the treatment of linear differential equations. If, for example, we wish to solve the differential equation ay + by + cy = 0, the equation is written in the notation (aD2 + bD + c)y = 0. Then, regarding D as an unknown quantity rather than an operator, we solve the algebraic quadratic equation aD2 + bD + c = 0. There are many other situations in which Boole, in his Treatise on Differential Equations of 1859, pointed out parallels between the properties of the differential operator (and its inverse) and the rules of algebra. British mathematicians in the second half of the nineteenth century were thus again becoming leaders in algorithmic analysis, a field in which, fifty years earlier, they had been badly deficient.
 

Odabrane stranice

Ostala izdanja - Prikaži sve

Uobičajeni izrazi i fraze

Popularni odlomci

Stranica 485 - New Edition. Crown 8vo. $s. KEY TO PLANE TRIGONOMETRY. Crown 8vo. los. 6d. A TREATISE ON SPHERICAL TRIGONOMETRY. New Edition, enlarged. Crown 8vo. 4-?. 6d. PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.
Stranica 489 - CAMPBELL : — THE NATURE OF THE ATONEMENT AND ITS RELATION TO REMISSION OF SINS AND ETERNAL LIFE. Fourth and Cheaper Edition, crown 8vo. 6s. "Among the first theological treatises of this generation.
Stranica 488 - Archer).— Works by the Rev. WILLIAM ARCHER BUTLER, MA, late Professor of Moral Philosophy in the University of Dublin : SERMONS, DOCTRINAL AND PRACTICAL. Edited, with a Memoir of the Author's Life, by THOMAS WOODWARD, Dean of Down.

Bibliografski podaci