On the application of integral equations to the determination of upper and lower limits to the value of a double integral. with: The solution of linear differential equations by means of definite integrals. with: The determination of solutions of the equation of wave motion involving an arbitrary function of three variables which satisfies a partial differential equation.

In: Transactions of the Cambridge Philosophical Society, Volume XXI. Cambridge:: University Press, 1912., 1912. 280 x 229 mm. 4to. Pages 123-128; 171-196; 257-280. [Entire volume: vi, 481 pp.] Full brown cloth; lightly freckled, spine ends frayed. Blind stamp of the Carnegie Institution, Washington, D.C. Very good. FIRST EDITIONS. "General theories had little attraction for Bateman; he was a master of the special instance. Much of his work consisted of finding special functions to solve partial differential equations. . .. Bateman's most significant single contribution to mathematical physics was a paper (1909) in which, following the work of Lorentz and Einstein on the invariance of the equations of electromagnetism under change of coordinates of constant velocity and constant acceleration, he showed that the most general group of transformations which reserve the electromagnetic equations and total charge of the system and are independent of the electromagnetic field is the group of conformal maps of four-dimensional space." DSB, I, pp. 499-500. Bateman was given a PhD by Johns Hopkins in 1913, a year after this paper, and it is highly irregular that he had more than60 published papers to his name already by the time of his advanced degree – an astonishing achievement for a PhD student. He was already “an extremely eminent mathematician” [MacTutor]. Among his few other interests, one was chess – which he played competitively.