Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as weIlas the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in AppliedMathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein­ force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and en­ courage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the AppliedMathematical Sei­ ences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface This book is designed to serve as a textbook for graduate students or advanced undergraduates studying numerical methods for the solution of partial differen­ tial equations goveming wave-like flows. Although the majority of the schemes presented in this text were introduced ineither the applied-rnathematics or atmos­ pheric-science literature, the focus is not on the nuts-and-bolts details of various atmospheric models but on fundamental numerical methods that have applications in a wide range of scientific and engineering disciplines.