Calculus of Finite Differences
Cód:
491_9781443728805
Originally published in 1800. CALCULUS OF FINITE DIFFERENCES by GEORGE BOOLE. PREFACE: IN the following exposition of the Calculus of Finite Dif ferences, particular attention has been paid to the connexion of its methods with those of the Differential Calculus a connexion which in some instances involves far more than a merely formal analogy. Indeed the work is in some measure designed as a sequel to my Treatise on Differential Equations. And it has been composed on the same plan. Mr Stirling, of Trinity College, Cambridge, has rendered me much valuable assistance in the revision of the proof sheets. In offering him my best thanks for his kind aid, I am led to express a hope that the work will be found to bo free from important errors. GEORGE BOOLE. QUEENS COLLKOE, CORK, April 18, 1800. PREFACE TO THE SECOND EDITION: WHEN I commenced to prepare for the press a Second Edition of the late Dr Booles Treatise on Finite Differ ences, my intention was to leave the work unchanged save by the insertion of sundry additions in the shape of para graphs marked off from the rest of the text. But I soon found that adherence to such a principle would greatly lessen the value of the book as a Text-book, since it would be impossible to avoid confused arrangement and even much repetition. I have therefore allowed myself considerable freedom as regards the form and arrangement of those parts where the additions are considerable, but I have strictly adhered to the principle of inserting all that was contained in the First Edition. As such Treatises as the present are in close connexion with the course of Mathematical Study at the University of Cambridge, there is considerable difficulty in deciding the question how far they should aim at being exhaustive. I have held it best not to insert investigations that involve complicated analysis unless they possess great suggestiveness or are the bases of important developments of the subject. Under the present system the premium on wide sup
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