Ueber ein die Flächen Kleinsten Flächeninhalts betreffendes Problem der Variationsrechnung. Festschrift zum jubelgeburtstage des Herrn Karl Weierstrass.

Helsingfors: Finnischen Literatur-Gesellschaft, 1885.

A fine copy of his path-breaking memoir in which he first derived the Cauchy-Schwarz inequality – “one of the most widely used and most important inequalities in all of mathematics.” (J.Michael Steele).

“In his most important work, a Festschrift for Weierstrass’ seventieth birthday, Schwarz set himself the task of completely answering the question of whether a given minimal surface really yields a minimal area. Aside from the achievement itself, which contains the first complete treatment of the second variation in a multiple integral, this work introduced methods that immediately became extremely fruitful. For example, a function was constructed through successive approximations that Picard was able to employ in obtaining his existence proof for differential equations. Furthermore, Schwarz demonstrated the existence of a certain number, which could be viewed as the (least) eigenvalue for the eigenvalue problem of a certain differential equation (these concepts did not exist then). This was done through a method that Schwarz’s student Erhard Schmidt later applied to the proof of the existence of an eigenvalue of an integral equation—a procedure that is one of the most important tools of modern analysis. In this connection Schwarz also employed the inequality for integrals that is today known as ‘Schwarz’s inequality’.” (DSB XII:246).

J. Michael Steele, The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities, p.1.

Large 4to: 285 x 225 mm. Original printed wrappers, small piece of the upper right corner of the front and rear wrapper missing, faint rubber stamp and a small closed tear to the bottom of front, otherwise fine and clean. In all a fine copy.

Item #2629

Price: $650.00