This book is printed on acid free paper.Ĭopyright O 2002 John Wiley & Sons, Inc. and printed and bound by Hamilton Printing. New York / Chichester / Weinheim / Brisbane / Singapore / TorontoĪcquisitions Editor Wayne Anderson Marketing Manager Katherine Hepburn Senior Production Editor Petrina Kulek Director Design Madelyn Lesure Illustration Coodinator Gene Aiello This book was set in Palatino by UG / GGS Information Services, Inc. Lightfoot Chemical Engineering Department University of Wisconsin-Madison This Page Intentionally Intentionally Left Left Blank Note: the differential operations may not be simply generalized to curvilinear coordinates see Tables A.7-2 and A.7-3.

**.DIFFERENTIAL OPERATIONS FOR SCALARS, VECTORS, AND TENSORS IN CARTESIAN COORDINATESĭ2vz d2v, d2vZ +-az2 ,= ,= ax2 + dvx dvx dvx ,= vx dx + vY dy + v, dz. Descriptions of curvilinear coordinates are given in Figures 1.2-2, A.6-1, A.8-1, and A.8-2. Note: The above operations may be generalized to cylindrical coordinates by replacing (x, y, z ) by (r, 6, z), and to spherical coordinates by replacing (x, y, z) by ( r, 6, 4). (s is a scalar v and w are vectors T is a tensor dot or cross operations enclosed within parentheses are scalars, those enclosed in brackets are vectors) ALGEBRAIC OPERATIONS FOR VECTORS AND TENSORS IN CARTESIAN COORDINATES l

Introducing the mattson 2 rar