A Treatise on Differential Equations, Band 2

Macmillan, 1865 - 85 Seiten
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.

Was andere dazu sagen - Rezension schreiben

Es wurden keine Rezensionen gefunden.

Ausgewählte Seiten

Andere Ausgaben - Alle anzeigen

Häufige Begriffe und Wortgruppen

Beliebte Passagen

Seite 20 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.
Seite 9 - The Fairy Book ; the Best Popular Fairy Stories. Selected and rendered anew by the Author of
Seite 10 - Christ and other Masters. A Historical Inquiry into some of the Chief Parallelisms and Contrasts between Christianity and the Religious Systems of the Ancient World.
Seite 11 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Seite 8 - Meteorographica, or Methods of Mapping the Weather. Illustrated by upwards of 600 Printed Lithographed Diagrams. By FRANCIS GALTON, FRS 4to.
Seite 30 - HELLENICA; OR, A HISTORY OF GREECE IN GREEK, as related by Diodorus and Thucydides ; being a First Greek Reading Book, with explanatory Notes, Critical and Historical.
Seite 11 - Crown 8vo. 7s. 6d. HOWARD. — The Pentateuch ; Or, the Five Books of Moses. Translated into English from the Version of the LXX. With Notes on its Omissions and Insertions, and also on the Passages in which it differs from the Authorized Version. By the Hon. HENRY HOWARD, DD Crown 8vo. GENESIS, One Volume, 8s. 6d. ; EXODUS AND LEVITICUS, One Volume, 10s. 6d. ; NUMBERS AND DEUTERONOMY, One Volume, 10s. 6d. HoziER. — The Seven 'Weeks' War ; Its Antecedents and its Incidents.
Seite 30 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Seite 19 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.

Bibliografische Informationen