Ordinary Differential Equations [antikvár]

Preface for the Teacher In writing this book, it has been our aim to make it readable for the student, to include topics of increasing importance (such as transforms, numerical analysis, the perturbation concept) and to avoid the errors traditionally transmitted in an elementary text. In this last connection, we have abandoned the use of the terminology "general solution" of a differential equation unless the solution is in fact general, i.e., unless the solution actually contains every solution of the differential equation. We have also avoided the term "singular solution." We have exercised great care in defining function, differentials and solutions; in particular we have tried to make it clear that functions have domains. On the other hand, this accuracy has been secondary to our main purpose: to teach the student how to use differential equations. We hope and believe that we have not overlooked any of the major applications which can be made comprehensible at this elementary level. You will find in this text an extensive list of worked examples and homework problems with answers. We acknowledge our indebtedness to the publishers for their cooperation and willingness to let us use new pedagogical devices and to Prof. C. A. Hutchinson for his thorough editing. M.T. H.P. Ithaca, New York West Lafayette, Indiana Preface for the Student This book has been written primarily for you, the student. We have tried to make it easy to read and easy to follow. We do not wish to imply, however, that you will be able to read this text as if it were a novel. If you wish to derive any benefit from it, you must study each page slowly and carefully. You must have pencil and plenty of paper beside you so that you yourself can reproduce each step and equation in an argument. When we say "verify a statement," "make a substitution," "add two equations," "multiply two factors," etc., you yourself must actually perform these operations. If you carry out the explicit and detailed instructions we have given you, we can almost guarantee that you will, with relative ease, reach the conclusion. One final suggestion—as you come across formulas, record them and their equation numbers on a separate sheet of paper for easy reference. You may also find it advantageous to do the same for Definitions and Theorems. M.T. H.P. Ithaca, New York West Lafayette, Indiana