![]() ![]() Some figures have been improved where the precise shape is significant the computer has been employed to achieve accuracy. Second, since time may not permit the inclusion of all the applications, those sections that can be omitted without disrupting the continuity have been starred. ![]() Thereby instructors are freer to choose the topics they deem most appropriate. Since not all classes go at the same pace or have the same objectives the two volumes of the first edition have been replaced by the present single volume. However, it does seem desirable, because students are weak in algebra, to keep the algebra simple at the outset while students are acquiring the concepts of the calculus. The pace of the first few chapters has been speeded up somewhat. Admittedly, a useful notation in showing the variables involved, it also suggests that the derivative is a quotient, whereas we must take great pains to convince the student that it is not. The use of dy / dx from the outset is the result of numerous requests. The notation ∫y dx has been introduced early to denote antidifferentiation. The notation has been restricted to the customary situation where time is the independent variable in other situations y′, dy / dx and f′(x) are used. Some changes in notation are unquestionably an improvement. Chapter 9, “The Definite Integral,” has been moved forward so that students using the mathematics in another course taken simultaneously can utilize the concept sooner. More use has been made of vector analysis, particularly in treating velocity and acceleration. A chapter on differential equations and a section on such numerical methods as Simpson’s rule and the trapezoidal rule have also been added. Hopefully the students will read the text instead of mechanically following the technique of the usual illustrative example. To counter this many illustrative examples are incorporated into the text instead of being set apart formally. Students doing homework exercises acquire the habit of searching for an illustrative example which they can imitate and thereby do the exercises without thinking. More drill exercises have been added, the exercises have been carefully graded as to difficulty, and there are more illustrative examples. In addition to extending the scope of the applications, I have made a number of other improvements. But since students have no idea of how these quantities are used, the only consequence is that the gravity of the problems produces inertia in the students. Many calculus texts dispose of applications by asking students to calculate centers of gravity and moments of inertia. Moreover, since most students who take calculus will be scientists or engineers, they will be highly motivated by the applications. The theory and technique of the calculus are, in themselves, meaningless. Several sections on physical applications have been dropped and applications to the social and biological sciences have been added instead. Most of the applications still belong with the physical sciences however, no knowledge of physics is presupposed. The rigorous approach should be reserved for a course in advanced calculus for mathematicians. Rigor undoubtedly refines the intuition but does not supplant it. Though this chapter could be used in conjunction with the opening chapters of the book, I do not recommend doing so the rigorous presentation is difficult to grasp and obscures the understanding. As to the approach, the last chapter introduces a rigorous treatment. The basic features of the first edition have been retained, such as the intuitive approach and real applications. Morris Kline 1908–1992 Mathematician, Educator 98-36211 QA303.K68 1998 CIP 515-dc21 Manufactured in the United States by Courier Corporation 40453609 Dedicated to the memory of “An unabridged republication of the work originally published in 1977 by John Wiley and Sons, Inc., New York”-T.p. Readers who would like to receive the solutions to the exercises may request them from the publisher at the following e-mail address: Library of Congress Cataloging-in-Publication Data Kline, Morris, 1908– Calculus : an intuitive and physical approach, second edition / Morris Kline. Bibliographical Note This Dover edition, first published in 1998, is an unabridged republication of the work originally published in 1977 by John Wiley and Sons, Inc., New York. Mineola, New YorkĬopyright Copyright © 1967, 1977 by John Wiley & Sons, Inc. CALCULUS An Intuitive and Physical ApproachĭOVER PUBLICATIONS, INC.
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