ebook img

Thomas' Calculus in SI Units PDF

1244 Pages·2019·102.645 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Thomas' Calculus in SI Units

GLOBAL This is a special edition of an established title widely used by colleges and GLOBAL universities throughout the world. Pearson published this exclusive edition EDITION for the benefit of students outside the United States. If you purchased EDITION EG this book within the United States, you should be aware that it has been DL ITO imported without the approval of the Publisher or Author. IOB A NL T H O M Thomas’ Calculus provides a modern introduction to calculus that helps students A develop conceptual understanding of the underlying mathematical ideas. The S ’ text continues to help students go beyond memorizing formulas by focusing on C • intuitive and precise explanations, thoughtfully chosen exercises and projects, and A detailed solutions; and • clear, easy-to-understand examples and the application of each new topic to real- L world problems. C The fourteenth edition features updated graphics, additional examples, and new types of homework exercises to help students visualize mathematical concepts U CALCULUS clearly, overcome conceptual obstacles, and acquire diffe ent perspectives on each topic. L THOMAS’ U Fourteenth Edition in SI Units S Hass • Heil • Weir F o u r in Stee I Unt h n itsEd it io n WHH ea eiril ss Hass_14_1292253223_Final.indd 1 05/02/19 5:13 PM THOMAS’ CALCULUS FOURTEENTH EDITION IN SI UNITS Based on the original work by GEORGE B. THOMAS, JR. Massachusetts Institute of Technology as revised by JOEL HASS University of California, Davis CHRISTOPHER HEIL Georgia Institute of Technology MAURICE D. WEIR Naval Postgraduate School SI conversion by JOSÉ LUIS ZULETA ESTRUGO École Polytechnique Fédérale de Lausanne A01_HASS3220_14_GE_FM.indd 1 07/02/19 3:02 PM Director, Portfolio Management: Deirdre Lynch Senior Author Support/Technology Specialist: Joe Vetere Executive Editor: Jeff Weidenaar Rights and Permissions Project Manager: Gina M. Cheselka Editorial Assistant: Jennifer Snyder Manufacturing Buyer: Carol Melville, LSC Communications, Inc. Content Producer: Rachel S. Reeve Program Design Lead: Barbara T. Atkinson Managing Producer: Scott Disanno Associate Director of Design: Blair Brown Producer: Stephanie Green Senior Manufacturing Controller, Global Edition: Caterina Pellegrino TestGen Content Manager: Mary Durnwald Editor, Global Edition: Subhasree Patra Manager: Content Development, Math: Kristina Evans Production Coordination, Composition: Pearson CSC Product Marketing Manager: Emily Ockay Cover Design: Lumina Datamatics Ltd. Field Marketing Manager: Evan St. Cyr Illustrations: Network Graphics, Cenveo® Publisher Services Marketing Assistants: Jennifer Myers, Erin Rush Cover Image: Brian Kenney/Shutterstock Attributions of third party content appear on page C-1, which constitutes an extension of this copyright page. PEARSON, ALWAYS LEARNING, and MYLAB MATH are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S. and/or other countries. Pearson Education Limited KAO Two KAO Park Harlow CM17 9NA United Kingdom and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsonglobaleditions.com © Pearson Education Limited, 2020 The rights of Joel Hass, Christopher Heil, and Maurice Weir to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Authorized adaptation from the United States edition, entitled Thomas’ Calculus, 14th Edition, ISBN 978-0-13-443898-6 by Joel Hass, Christopher Heil, and Maurice Weir, published by Pearson Education, Inc., © 2018, 2014, 2010. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. For information regarding per- missions, request forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please visit www.pearsoned.com/permissions. This eBook is a standalone product and may or may not include all assets that were part of the print version. It also does not provide access to other Pearson digital products like MyLab and Mastering. The publisher reserves the right to remove any material in this eBook at any time. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN 10: 1-292-25322-3 ISBN 13: 978-1-292-25322-0 eBook ISBN 13: 978-1-292-25329-9 Typeset by Integra Software Services. A01_HASS3220_14_GE_FM.indb 2 3/4/19 6:04 PM Contents Preface 9 1 Functions 19 1.1 Functions and Their Graphs 19 1.2 Combining Functions; Shifting and Scaling Graphs 32 1.3 Trigonometric Functions 39 1.4 Graphing with Software 47 Questions to Guide Your Review 51 Practice Exercises 52 Additional and Advanced Exercises 53 Technology Application Projects 55 2 Limits and Continuity 56 2.1 Rates of Change and Tangent Lines to Curves 56 2.2 Limit of a Function and Limit Laws 63 2.3 The Precise Definition of a Limit 74 2.4 One-Sided Limits 83 2.5 Continuity 90 2.6 Limits Involving Infinity; Asymptotes of Graphs 101 Questions to Guide Your Review 114 Practice Exercises 115 Additional and Advanced Exercises 116 Technology Application Projects 119 3 Derivatives 120 3.1 Tangent Lines and the Derivative at a Point 120 3.2 The Derivative as a Function 124 3.3 Differentiation Rules 133 3.4 The Derivative as a Rate of Change 142 3.5 Derivatives of Trigonometric Functions 152 3.6 The Chain Rule 158 3.7 Implicit Differentiation 166 3.8 Related Rates 171 3.9 Linearization and Differentials 180 Questions to Guide Your Review 192 Practice Exercises 192 Additional and Advanced Exercises 197 Technology Application Projects 200 3 A01_HASS3220_14_GE_FM.indd 3 07/02/19 3:02 PM 4 Contents 4 Applications of Derivatives 201 4.1 Extreme Values of Functions on Closed Intervals 201 4.2 The Mean Value Theorem 209 4.3 Monotonic Functions and the First Derivative Test 215 4.4 Concavity and Curve Sketching 220 4.5 Applied Optimization 232 4.6 Newton’s Method 244 4.7 Antiderivatives 249 Questions to Guide Your Review 259 Practice Exercises 259 Additional and Advanced Exercises 262 Technology Application Projects 265 5 Integrals 266 5.1 Area and Estimating with Finite Sums 266 5.2 Sigma Notation and Limits of Finite Sums 276 5.3 The Definite Integral 283 5.4 The Fundamental Theorem of Calculus 296 5.5 Indefinite Integrals and the Substitution Method 307 5.6 Definite Integral Substitutions and the Area Between Curves 314 Questions to Guide Your Review 324 Practice Exercises 325 Additional and Advanced Exercises 328 Technology Application Projects 331 6 Applications of Definite Integrals 332 6.1 Volumes Using Cross-Sections 332 6.2 Volumes Using Cylindrical Shells 343 6.3 Arc Length 351 6.4 Areas of Surfaces of Revolution 356 6.5 Work and Fluid Forces 362 6.6 Moments and Centers of Mass 371 Questions to Guide Your Review 383 Practice Exercises 384 Additional and Advanced Exercises 386 Technology Application Projects 387 7 Transcendental Functions 388 7.1 Inverse Functions and Their Derivatives 388 7.2 Natural Logarithms 396 7.3 Exponential Functions 404 7.4 Exponential Change and Separable Differential Equations 415 7.5 Indeterminate Forms and L’Hôpital’s Rule 425 7.6 Inverse Trigonometric Functions 434 7.7 Hyperbolic Functions 446 A01_HASS3220_14_GE_FM.indd 4 07/02/19 3:02 PM Contents 5 7.8 Relative Rates of Growth 454 Questions to Guide Your Review 459 Practice Exercises 460 Additional and Advanced Exercises 463 8 Techniques of Integration 465 8.1 Using Basic Integration Formulas 465 8.2 Integration by Parts 470 8.3 Trigonometric Integrals 478 8.4 Trigonometric Substitutions 484 8.5 Integration of Rational Functions by Partial Fractions 489 8.6 Integral Tables and Computer Algebra Systems 497 8.7 Numerical Integration 503 8.8 Improper Integrals 512 Questions to Guide Your Review 523 Practice Exercises 524 Additional and Advanced Exercises 526 Technology Application Projects 529 9 Infinite Sequences and Series 530 9.1 Sequences 530 9.2 Infinite Series 543 9.3 The Integral Test 553 9.4 Comparison Tests 559 9.5 Absolute Convergence; The Ratio and Root Tests 564 9.6 Alternating Series and Conditional Convergence 571 9.7 Power Series 578 9.8 Taylor and Maclaurin Series 589 9.9 Convergence of Taylor Series 594 9.10 Applications of Taylor Series 601 Questions to Guide Your Review 610 Practice Exercises 611 Additional and Advanced Exercises 613 Technology Application Projects 615 10 Parametric Equations and Polar Coordinates 616 10.1 Parametrizations of Plane Curves 616 10.2 Calculus with Parametric Curves 625 10.3 Polar Coordinates 634 10.4 Graphing Polar Coordinate Equations 638 10.5 Areas and Lengths in Polar Coordinates 642 10.6 Conic Sections 647 10.7 Conics in Polar Coordinates 655 Questions to Guide Your Review 661 Practice Exercises 662 Additional and Advanced Exercises 664 Technology Application Projects 666 A01_HASS3220_14_GE_FM.indd 5 07/02/19 3:02 PM 6 Contents 11 Vectors and the Geometry of Space 667 11.1 Three-Dimensional Coordinate Systems 667 11.2 Vectors 672 11.3 The Dot Product 681 11.4 The Cross Product 689 11.5 Lines and Planes in Space 695 11.6 Cylinders and Quadric Surfaces 704 Questions to Guide Your Review 710 Practice Exercises 710 Additional and Advanced Exercises 712 Technology Application Projects 715 12 Vector-Valued Functions and Motion in Space 716 12.1 Curves in Space and Their Tangents 716 12.2 Integrals of Vector Functions; Projectile Motion 725 12.3 Arc Length in Space 734 12.4 Curvature and Normal Vectors of a Curve 738 12.5 Tangential and Normal Components of Acceleration 744 12.6 Velocity and Acceleration in Polar Coordinates 750 Questions to Guide Your Review 754 Practice Exercises 755 Additional and Advanced Exercises 757 Technology Application Projects 758 13 Partial Derivatives 759 13.1 Functions of Several Variables 759 13.2 Limits and Continuity in Higher Dimensions 767 13.3 Partial Derivatives 776 13.4 The Chain Rule 788 13.5 Directional Derivatives and Gradient Vectors 798 13.6 Tangent Planes and Differentials 806 13.7 Extreme Values and Saddle Points 816 13.8 Lagrange Multipliers 825 13.9 Taylor’s Formula for Two Variables 835 13.10 Partial Derivatives with Constrained Variables 839 Questions to Guide Your Review 843 Practice Exercises 844 Additional and Advanced Exercises 847 Technology Application Projects 849 A01_HASS3220_14_GE_FM.indd 6 07/02/19 3:02 PM Contents 7 14 Multiple Integrals 850 14.1 Double and Iterated Integrals over Rectangles 850 14.2 Double Integrals over General Regions 855 14.3 Area by Double Integration 864 14.4 Double Integrals in Polar Form 867 14.5 Triple Integrals in Rectangular Coordinates 874 14.6 Applications 884 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 894 14.8 Substitutions in Multiple Integrals 906 Questions to Guide Your Review 916 Practice Exercises 916 Additional and Advanced Exercises 919 Technology Application Projects 921 15 Integrals and Vector Fields 922 15.1 Line Integrals of Scalar Functions 922 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 929 15.3 Path Independence, Conservative Fields, and Potential Functions 942 15.4 Green’s Theorem in the Plane 953 15.5 Surfaces and Area 965 15.6 Surface Integrals 975 15.7 Stokes’ Theorem 985 15.8 The Divergence Theorem and a Unified Theory 998 Questions to Guide Your Review 1011 Practice Exercises 1011 Additional and Advanced Exercises 1014 Technology Application Projects 1015 16 First-Order Differential Equations 1016 16.1 Solutions, Slope Fields, and Euler’s Method 1016 16.2 First-Order Linear Equations 1024 16.3 Applications 1030 16.4 Graphical Solutions of Autonomous Equations 1036 16.5 Systems of Equations and Phase Planes 1043 Questions to Guide Your Review 1049 Practice Exercises 1049 Additional and Advanced Exercises 1051 Technology Application Projects 1052 A01_HASS3220_14_GE_FM.indd 7 07/02/19 3:02 PM 8 Contents 17 Second-Order Differential Equations (Online) 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendices AP-1 A.1 Real Numbers and the Real Line AP-1 A.2 Mathematical Induction AP-6 A.3 Lines, Circles, and Parabolas AP-9 A.4 Proofs of Limit Theorems AP-19 A.5 Commonly Occurring Limits AP-22 A.6 Theory of the Real Numbers AP-23 A.7 Complex Numbers AP-26 A.8 Probability AP-34 A.9 The Distributive Law for Vector Cross Products AP-47 A.10 The Mixed Derivative Theorem and the Increment Theorem AP-49 Answers to Odd-Numbered Exercises A-1 Credits C-1 Applications Index AI-1 Subject Index SI-1 A Brief Table of Integrals T-1 Basic Algebra Formulas B-1 Limits, Differentiation, and Integration Rules L-2 A01_HASS3220_14_GE_FM.indd 8 07/02/19 3:02 PM Preface Thomas’ Calculus, Fourteenth Edition in SI Units, provides a modern introduction to cal- culus that focuses on developing conceptual understanding of the underlying mathematical ideas. This text supports a calculus sequence typically taken by students in STEM fields over several semesters. Intuitive and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets are the foundation of this text. We continue to improve this text in keeping with shifts in both the preparation and the goals of today’s students, and in the applications of calculus to a changing world. Many of today’s students have been exposed to calculus in high school. For some, this translates into a successful experience with calculus in college. For others, however, the result is an overconfidence in their computational abilities coupled with underlying gaps in algebra and trigonometry mastery, as well as poor conceptual understanding. In this text, we seek to meet the needs of the increasingly varied population in the calculus sequence. We have taken care to provide enough review material (in the text and appen- dices), detailed solutions, and a variety of examples and exercises, to support a complete understanding of calculus for students at varying levels. Within the text, we present the material in a way that supports the development of mathematical maturity, going beyond memorizing formulas and routine procedures, and we show students how to generalize key concepts once they are introduced. References are made throughout, tying new concepts to related ones that were studied earlier. After studying calculus from Thomas, students will have developed problem-solving and reasoning abilities that will serve them well in many important aspects of their lives. Mastering this beautiful and creative subject, with its many practical applications across so many fields, is its own reward. But the real gifts of studying calculus are acquiring the ability to think logically and precisely; understand- ing what is defined, what is assumed, and what is deduced; and learning how to generalize conceptually. We intend this book to encourage and support those goals. New to This Edition We welcome to this edition a new coauthor, Christopher Heil from the Georgia Institute of Technology. He has been involved in teaching calculus, linear algebra, analysis, and abstract algebra at Georgia Tech since 1993. He is an experienced author and served as a consultant on the previous edition of this text. His research is in harmonic analysis, includ- ing time-frequency analysis, wavelets, and operator theory. This is a substantial revision. Every word, symbol, and figure was revisited to en- sure clarity, consistency, and conciseness. Additionally, we made the following text-wide updates: 9 A01_HASS3220_14_GE_FM.indd 9 07/02/19 3:02 PM

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.