Preface to the First Edition We call this book Numerical Recipes for several reasons.In one sense,this book is indeed a "cookbook"on numerical computation.However there is an important distinction between a cookbook and a restaurant menu.The latter presents choices among complete dishes in each of which the individual flavors are blended and disguised.The former-and this book-reveals the individual ingredients and explains how they are prepared and combined. Another purpose of the title is to connote an eclectic mixture of presentational techniques.This book is unique,we think,in offering,for each topic considered, a certain amount of general discussion,a certain amount of analytical mathematics NUMERICAL a certain amount of discussion of algorithmics,and (most important)actual imple- mentations of these ideas in the form of working computer routines.Our task has been to find the right balance among these ingredients for each topic.You will find that for some topics we have tilted quite far to the analytic side;this where we have felt there to be gaps in the"standard"mathematical training.For other topics, (North. where the mathematical prerequisites are universally held,we have tilted towards more in-depth discussion of the nature of the computational algorithms,or towards 、子学三今 practical questions of implementation. We admit,therefore,to some unevenness in the"level"of this book.About half F8 of it is suitable for an advanced undergraduate course on numerical computation for science or engineering majors.The other half ranges from the level of a graduate g course to that of a professional reference.Most cookbooks have,after all,recipes at varying levels of complexity.An attractive feature of this approach,we think,is that the reader can use the book at increasing levels of sophistication as his/her experience 6 grows.Even inexperienced readers should be able to use our most advanced routines as black boxes.Having done so,we hope that these readers will subsequently go back and learn what secrets are inside. If there is a single dominant theme in this book,it is that practical methods of numerical computation can be simultaneously efficient,clever,and-important -clear.The alternative viewpoint,that efficient computational methods must necessarily be so arcane and complex as to be useful only in "black box"form, we firmly reject. 。 Our purpose in this book is thus to open up a large number of computational black boxes to your scrutiny.We want to teach you to take apart these black boxes and to put them back together again,modifying them to suit your specific needs Software. We assume that you are mathematically literate,i.e.,that you have the normal mathematical preparation associated with an undergraduate degree in a physical science,or engineering,or economics,or a quantitative social science.We assume America). that you know how to program a computer.We do not assume that you have any machine- prior formal knowledge of numerical analysis or numerical methods. The scope of Numerical Recipes is supposed to be "everything up to,but not including,partial differential equations."We honor this in the breach:First, we do have one introductory chapter on methods for partial differential equations (Chapter 19).Second,we obviously cannot include everything else.All the so-called "standard"topics of a numerical analysis course have been included in this book: XIVPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). Preface to the First Edition We call this book Numerical Recipesfor several reasons. In one sense, this book is indeed a “cookbook” on numerical computation. However there is an important distinction between a cookbook and a restaurant menu. The latter presents choices among complete dishes in each of which the individual flavors are blended and disguised. The former — and this book — reveals the individual ingredients and explains how they are prepared and combined. Another purpose of the title is to connote an eclectic mixture of presentational techniques. This book is unique, we think, in offering, for each topic considered, a certain amount of general discussion, a certain amount of analytical mathematics, a certain amount of discussion of algorithmics, and (most important) actual imple￾mentations of these ideas in the form of working computer routines. Our task has been to find the right balance among these ingredients for each topic. You will find that for some topics we have tilted quite far to the analytic side; this where we have felt there to be gaps in the “standard” mathematical training. For other topics, where the mathematical prerequisites are universally held, we have tilted towards more in-depth discussion of the nature of the computational algorithms, or towards practical questions of implementation. We admit, therefore, to some unevenness in the “level” of this book. About half of it is suitable for an advanced undergraduate course on numerical computation for science or engineering majors. The other half ranges from the level of a graduate course to that of a professional reference. Most cookbooks have, after all, recipes at varying levels of complexity. An attractive feature of this approach, we think, is that the reader can use the book at increasing levels of sophistication as his/her experience grows. Even inexperienced readers should be able to use our most advanced routines as black boxes. Having done so, we hope that these readers will subsequently go back and learn what secrets are inside. If there is a single dominant theme in this book, it is that practical methods of numerical computation can be simultaneously efficient, clever, and — important — clear. The alternative viewpoint, that efficient computational methods must necessarily be so arcane and complex as to be useful only in “black box” form, we firmly reject. Our purpose in this book is thus to open up a large number of computational black boxes to your scrutiny. We want to teach you to take apart these black boxes and to put them back together again, modifying them to suit your specific needs. We assume that you are mathematically literate, i.e., that you have the normal mathematical preparation associated with an undergraduate degree in a physical science, or engineering, or economics, or a quantitative social science. We assume that you know how to program a computer. We do not assume that you have any prior formal knowledge of numerical analysis or numerical methods. The scope of Numerical Recipes is supposed to be “everything up to, but not including, partial differential equations.” We honor this in the breach: First, we do have one introductory chapter on methods for partial differential equations (Chapter 19). Second, we obviously cannot include everything else. All the so-called “standard” topics of a numerical analysis course have been included in this book: xiv