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Advanced Engineering Mathematics

San Diego San Francisco New York BostonLondon Toronto Sydney TokyoAlan JeffreyUniversity of Newcastle-upon-TyneSponsoring EditorBarbara HollandProduction EditorJulie BolducPromotions ManagerStephanie StevensCover DesignMonty Lewis DesignText DesignThompson Steele Production ServicesFront Matter DesignPerspectivesCopyeditorKristin LandonCompositionTechBooksPrinterRR Donnelley & Sons, book is printed on acid-free paper. CopyrightC 2002 by HARCOURT/ACADEMIC PRESSAll rights part of this publication may be reproduced or transmitted in any form or by anymeans, electronic or mechanical, including photocopy, recording, or any informationstorage and retrieval system, without permission in writing from the for permission to make copies of any part of the work should be mailed to:Permissions Department, Harcourt, Inc.

CHAPTER17 Conformal Mapping and Applications to Boundary Value Problems 877 17.1 Conformal Mapping 877 17.2 Conformal Mapping and Boundary Value Problems 904 PART SEVEN PARTIAL DIFFERENTIAL EQUATIONS 925 CHAPTER18 Partial Differential Equations 927 18.1 What Is a Partial Differential Equation? 927 18.2 The Method of Characteristics 934

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more restricted applications required by physics. For example, Stokes’ theorem is usually applied by a physicist to a surface with the tacit understanding that it be simply connected.

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An equation is said to be linear if the unknown function and its deriva-tives are linear in F. For example, a(x,y)ux +b(x,y)uy +c(x,y)u = f(x,y), where the functions a, b, c and f are given, is a linear equation of first order. An equation is said to be quasilinear if it is linear in the highest deriva-tives. For example,

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