Linear Differential Operators

by Cornelius Lanczos

Don't let the title fool you! If you are interested in numerical analysis, applied mathematics, or the solution procedures for differential equations, you will find this book useful. Because of Lanczos' unique style of describing mathematical facts in nonmathematical language, Linear Differential Operators also will be helpful to nonmathematicians interested in applying the methods and techniques described. Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems.

Genres: Mathematics, Calculus

582 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."