To indicate some of the power of the methods introduced, a number Text so that they can see that there is a story behind the results, techniques, andĮxamples-that the subject coheres and that this coherence is important for problem solving. Consequently, I have written a rather expansive Multivariable calculus, for many students, represents the beginning of significant mathematical maturation. To begin exploration of the interrelations among analysis, geometry, and matrix Vector calculus is in many ways an ideal subject for students Variables, so these concrete and visual situations are emphasized to explicate the Important and motivational examples usually arise for functions of two and three Results in the case of n variables (where n is arbitrary), I recognize that the most Through the development of a good geometric intuition. I also believe that a conceptual understanding of mathematics can be obtained Reasoning by analogy will thus be an important pedagogical tool. In the calculus of several variables can look quite similar to those of the calculus Stated with reasonable levels of clarity and generality. Notation, so that many results, especially those of differential calculus, can be The first goal can be met, at least in part, through the use of vector and matrix My own objectives in writing the book are simple ones: to develop in studentsĪ sound conceptual grasp of vector calculus and to help them begin the transitionįrom first-year calculus to more advanced technical mathematics. Although the mathematical background assumed is not exceptional, the reader will still be challenged In particular, the necessary matrix arithmeticĪnd algebra (not linear algebra) are developed as needed. Sophomore-level course in multivariable calculus, is a standard course in the calculus of functions of one variable. The only technical prerequisite for this text, which is intended for a Is an exciting and beautiful subject in its own right, a true adventure in many Vector calculus is the essential mathematical tool for such analysis. Understand geometry in two, three, or more dimensions recognizes the need toĪnalyze changing quantities that depend on more than a single variable. Observes the trajectory of a particle or planet, or indeed anyone who seeks to To understand the vagaries of a nation’s employment cycles, the physicist who The sociologist or psychologist who studies group behavior, the economist who endeavors Physical and natural phenomena depend on a complex array of factors. Numerical Approximations of Multiple Integrals (optional)įurther Vector Analysis Maxwell’s Equations Gradient, Divergence, Curl, and the Del Operator Properties Higher-order Partial Derivatives To the Student: Some Preliminary Notationįunctions of Several Variables Graphing Surfaces Including the American Mathematical Society, the Mathematical Association of Professor Colley is a member of several professional and honorary societies, Internationally on her research and has taught a wide range of subjects in undergraduate mathematics. Professor Colley has published papers on algebraic geometry and commutative algebra, as well as articles on other mathematical subjects. Her research focuses on enumerative problems in algebraic geometry, particularly concerning multiple-point singularities and higher-order contact of plane Institute of Technology prior to joining the faculty at Oberlin in 1983. degrees in mathematics from the Massachusetts Oberlin College and currently Chair of the Department, having also previously Susan Colley is the Andrew and Pauline Delaney Professor of Mathematics at , Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to For information on obtaining permission for use of material in this work, please submit a written request Means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any – 4th ed.Ĭ 2012, 2006, 2002 Pearson Education, Inc.Īll rights reserved. Library of Congress Cataloging-in-Publication Data Where those designations appear in this book, and Pearson Education was aware of a trademarkĬlaim, the designations have been printed in initial caps or all caps. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as Production Coordination and Composition: Aptara, Inc.Ĭover Image: Alessandro Della Bella/AP Images Rights and Permissions Advisor: Michael Joyce Senior Author Support/Technology Specialist: Joe Vetere Senior Acquisitions Editor: William HoffmanĮxecutive Marketing Manager: Jeff Weidenaar Boston Columbus Indianapolis New York San Francisco Upper Saddle RiverĪmsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Torontoĭelhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
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