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Revealing, entertaining window on the music of the ’50s and ’60s
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Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Most of the plates printed on both sides. Published 1915.
Thousands of scenes photographed 1861-65, with text by many special authorities.
1. We begin by giving a simple example of a partial differential inequality that occurs in an elementary physics problem. We consider a fluid with pressure u(x, t) at the point x at the instant t that 3 occupies a region Q oflR bounded by a membrane r of negligible thickness that, however, is semi-permeable, i. e., a membrane that permits the fluid to enter Q freely but that prevents all outflow of fluid. One can prove then (cf. the details in Chapter 1, Section 2.2.1) that au (aZu azu aZu) (1) in Q, t>o, -a - du = g du = -a z + -a z + -a z t Xl X X3 z l g a given function, with boundary conditions in the form of inequalities u(X,t»o => au(x,t)/an=O, XEr, (2) u(x,t)=o => au(x,t)/an?:O, XEr, to which is added the initial condition (3) u(x,O)=uo(x). We note that conditions (2) are non linear; they imply that, at each fixed instant t, there exist on r two regions r~ and n where u(x, t) =0 and au (x, t)/an = 0, respectively. These regions are not prescribed; thus we deal with a "free boundary" problem.
Fought over the course of four years, the Civil War pitted countrymen against countrymen, North versus South, friend against friend, and brother against brother. The photographs within these pages document the war that united America as one. These rare shots were taken in the middle of the battlefield during the earliest days of photography. Selected from a collection of seven thousand original negatives, these historic photos capture nearly every aspect of Civil War life. Among these photos are images of camps sprawling across acres, soldiers at their battlements, firing of heavy artillery, the aftermath of battle, and the terror that these young men faced. See first-hand of Union and Confederate officers strategizing their next moves, and Abraham Lincoln addressing his Union commanders. Originally released from the private collection of Edward Bailey Eaton in 1907, this edition is a must have for any Civil War buff or historian. No collection can be considered complete without these photographs by Matthew Brady and Alexander Gardner, as well as the meticulous passages that put the images in illuminating context.