Linear Differential Operators

by Cornelius Lanczos

This graduate-level, self-contained text addresses the basic and characteristic properties of linear differential operators, examining ideas and concepts and their interrelations rather than mere manipulation of formulae. Written at an advanced level, the text requires no specific knowledge beyond the usual introductory courses, and some 350 problems and their solutions are included.

Genres: Mathematics, Calculus

576 pages, Paperback

First published January 1, 1987

Reviews

[David · Rating 4 out of 5]

This book is quirky -- what you'd expect from Lanczos were you acquainted with his other writing, but perhaps not what you'd expect if you were familiar with other books on the topic. Of the mathematics books on my shelf, it has one of my favorite openings. From the beginning of the Preface:
"In one of the (unfortunately lost) comedies of Aristophanes the Voice of the Mathematician appeared, as it descended from a snow-capped mountain peak, pronouncing in a ponderous sing-song -- and words which to the audience sounded like complete gibberish -- his eternal Theorems, Lemmas, and Corollaries. The laughter of the listeners was enhanced by the implication that in fifty years' time another Candidate of Eternity would pronounce from the same snow-capped mountain peak exactly the same theorems, although in a modified but scarcely less ponderous and incomprehensible language.
Since the days of antiquity it has been the privilege of the mathematician to engrave his conclusions, expressed in a rarefied and esoteric language, upon the rocks of eternity. While this method is excellent for the codification of mathematical results, it is not so acceptable to the many addicts of mathematics, for whom the science of mathematics is not a logical game, but the language in which the physical universe speaks to us, and whose mastery is inevitable for the comprehension of natural phenomena."