实例介绍
【实例简介】
本资料为纯英文版，是美国大学一元微积分入门教材 When the first edition of this book appeared twelve years ago, a heated debate about calculus reform was taking place. Such issues as the use of technology, the relevance of rigor, and the role of discovery versus that of drill were causing deep splits in mathematics departme
59725SVEror-EPSVFrontEP qk 11/22/08 3: 46 PM Page 2 REFERENCE PAGES TRIGONOMETRY Angle Measurement Fundamental identities T radians=180° sin e sec 8= 1 lrad=180° cos B sin e (e in radians) sin 0+ cos 0= 1 Right Angle Trigonometry 1+tan 0= sec-e 1 +cot 0= csce opp hyp Csc 0- hyp hyp sIn (-)=-sin cos(-0)=cos 0 cos b- sec 0- hyp T tan(-0)--tan 0 9- cos 0 di tan 0 ot 6 dj h sin g 9= cot e Trigonometric Functions The law of sines y C tan o= y cot 0= The law of cosines a=b+ci-2bc cos a Graphs of Trigonometric Functions b-a+c-2ac cos b y=tanx c2=a2-b--2ab cos c y=sin x 2丌 Addition and subtraction formulas in(x+ y)=sin x cos y+ cos x sin y sin(x - v)= sin x cosy- cos x sin y cos(x +y)=cos x cos y x sin y y=cot x cos(x-y)= cos x cos y+ sin x sin y 1- tan r tan TT I lan(x-y Double-Angle formula 2x=2 Trigonometric Functions of Important Angles cos 2x=cos'x- sin 2x=2 cos=x-I=1-2 sin2x d sin e tan A 1/2 √3/3 45° r/4 √2/2 Half-Angle Formul √3/2 1/2 √3 90° 1 2 59726SV_FM_FM pi-xxiii cK< 11/22/08 3: 08 PM Page i Single Variable Calculus Concepts and Contexts 4e 59726SV_FM__FM pi-xxiii c 11/ 22/08 3: 08 PM Calculus and the architecture of curves The cover photograph shows the DZ Bank in Berlin designed and built 1995-2001 by Frank Gehry and Associates the interior atrium is dominated by a curvaceous four- story stainless steel sculptural shell that suggests a prehistoric creature and houses a central con ference space The highly complex structures that frank gehry designs would be impossible to build without the computer. The Catia software that his archi- tects and engineers use to produce the computer models is based on principles of calculus-fitting curves by matching tangent lines, making sure the curvature isnt too large, and controlling parametric surfaces. Consequently says gehry we have a lot of freedom I can play with shapes The process starts with Gehry's initia sketches, which are translated into a succes sion of physical models. (Hundreds of different physical models were constructed during the design of the building first with basic wooden blocks and then evolving into more sculptural forms. )Then an engineer uses a digitizer to record the coordinates of a series of points on a physical model. The digitized points are fed into a computer and the Catia software is used to link these points with smooth curves. (It joins curves so that 理型还置国 their tangent lines coincide; you can use the same idea to design the shapes of letters in the Laboratory Project on page 208 of this book. )The architect has considerable free dom in creating these curves, guided by displays of the curve, its derivative, and its curvature. Then the curves are 59726SV_FM_FM pi-xxiii c< 11/22/08 3: 08 PM Page iii connected to each other by a parametric surface. The CAtia program was developed in france and again the architect can do so in many possible by Dassault Systemes, originally for designing ways with the guidance of displays of the geometric airplanes, and was subsequently employed in characteristics of the surface the automotive industry. Frank gehry, because of The Catia model is then used to produce his complex sculptural shapes, is the first to use another physical model, which, in turn, suggests it in architecture. It helps him answer his ques modifications and leads to additional computer tion,How wiggly can you get and still make a and physical models building? 59726SV_FM__ FM pi-xxiii cK< 11/ 22/08 3: 08 PM Page iv 59726SV_FM__ FM pi-xxiii cK< 11/ 22/08 3: 08 PM Page v Single Variable Calculus Concepts and Contexts 4e James stewart McMaster University University Toronto e BROOKS/COLE CENGAGE Learning Australia. Brazil Japan. Korea. Mexico. Singapore. Spain, United Kingdom. United States 59726SV_FM_ FM pi-xxiii cK< 11/22/08 3: 08 PM Page vi e BROOKS/COLE W CENGAGE Learning Single Variable Calculus: Concepts and Contexts, C)2010, 2005 Brooks/Cole, Cengage Learning Fourth edition 」 ames stewart ALL RIGHTS RESERVED. No part of this work covered by the copy right herein may be reproduced, transmitted, stored, or used in any Publisher: richard stratton form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, Senior Developmental Editor: Jay Campbell taping, Web distribution, information networks, or information Associate Editor: Jeannine Lawless storage and retrieval systems, except as permitted under Section Editorial assistant: Elizabeth Neustaetter 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. Media Editor: Peter galuardi Senior Marketing Manager: Jennifer Jones For product information and technology assistance, contact us at marketing Assistant: Angela Kim Cengage Learning Customer Sales Support, 1-800-354-9706 Marketing Communications Manager: Mary Anne Payumo For permission to use material from this text or product, Senior Project Manager, Editorial Production submitallrequestsonlineatwww.cengage.com/permissions. Cheryll Linthicum Further permissions questions can be e-mailed to permissionrequest@cengage.com. Creative Director: Rob hugel Senior art Director: Vernon boes Library of Congress Control Number 2008941253 Senior Print Buyer: Becky Cross SBN-13:978-0-495-55972-6 Permissions editor: Bob kauser SBN-10:0495559725 Production service: tECH arts Text Des g ner:」 anne Calabrese Photo Researcher: Pre-Press PMg Brooks/Cole 10 Davis Drive Copy Editor: Kathi Townes Belmont, CA 94002-3098 Illustrator: Brian Betsill Cover Designer: Irene Morris CoverImageandpageiv:thomasmayerarchive.com Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singa Compositor: Stephanie Kuhns, TECHarts pore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locateyourlocalofficeatwww.cengage.com/international Cengage Learning products are represented in Canada by Nelson education Ltd To learn more about brooks/ cole, visit www.cengage.com/brookscole Purchase any of our products at your local college store or at our preferredonlinestorewww.ichapters.com Trademarks Derive is a registered trademark of Soft Warehouse Ir Maple is a registered trademark of Waterloo Maple, Inc. Mathematica is a registered trademark of Wolfram Research, Inc Tools for Enriching is a trademark used herein under license Printed in Canada 12345671211100908 59726SV_FM__FM pi-xxiii c 11/ 22/08 3: 08 PM To li Li 【实例截图】
【核心代码】
本资料为纯英文版，是美国大学一元微积分入门教材 When the first edition of this book appeared twelve years ago, a heated debate about calculus reform was taking place. Such issues as the use of technology, the relevance of rigor, and the role of discovery versus that of drill were causing deep splits in mathematics departme
59725SVEror-EPSVFrontEP qk 11/22/08 3: 46 PM Page 2 REFERENCE PAGES TRIGONOMETRY Angle Measurement Fundamental identities T radians=180° sin e sec 8= 1 lrad=180° cos B sin e (e in radians) sin 0+ cos 0= 1 Right Angle Trigonometry 1+tan 0= sec-e 1 +cot 0= csce opp hyp Csc 0- hyp hyp sIn (-)=-sin cos(-0)=cos 0 cos b- sec 0- hyp T tan(-0)--tan 0 9- cos 0 di tan 0 ot 6 dj h sin g 9= cot e Trigonometric Functions The law of sines y C tan o= y cot 0= The law of cosines a=b+ci-2bc cos a Graphs of Trigonometric Functions b-a+c-2ac cos b y=tanx c2=a2-b--2ab cos c y=sin x 2丌 Addition and subtraction formulas in(x+ y)=sin x cos y+ cos x sin y sin(x - v)= sin x cosy- cos x sin y cos(x +y)=cos x cos y x sin y y=cot x cos(x-y)= cos x cos y+ sin x sin y 1- tan r tan TT I lan(x-y Double-Angle formula 2x=2 Trigonometric Functions of Important Angles cos 2x=cos'x- sin 2x=2 cos=x-I=1-2 sin2x d sin e tan A 1/2 √3/3 45° r/4 √2/2 Half-Angle Formul √3/2 1/2 √3 90° 1 2 59726SV_FM_FM pi-xxiii cK< 11/22/08 3: 08 PM Page i Single Variable Calculus Concepts and Contexts 4e 59726SV_FM__FM pi-xxiii c 11/ 22/08 3: 08 PM Calculus and the architecture of curves The cover photograph shows the DZ Bank in Berlin designed and built 1995-2001 by Frank Gehry and Associates the interior atrium is dominated by a curvaceous four- story stainless steel sculptural shell that suggests a prehistoric creature and houses a central con ference space The highly complex structures that frank gehry designs would be impossible to build without the computer. The Catia software that his archi- tects and engineers use to produce the computer models is based on principles of calculus-fitting curves by matching tangent lines, making sure the curvature isnt too large, and controlling parametric surfaces. Consequently says gehry we have a lot of freedom I can play with shapes The process starts with Gehry's initia sketches, which are translated into a succes sion of physical models. (Hundreds of different physical models were constructed during the design of the building first with basic wooden blocks and then evolving into more sculptural forms. )Then an engineer uses a digitizer to record the coordinates of a series of points on a physical model. The digitized points are fed into a computer and the Catia software is used to link these points with smooth curves. (It joins curves so that 理型还置国 their tangent lines coincide; you can use the same idea to design the shapes of letters in the Laboratory Project on page 208 of this book. )The architect has considerable free dom in creating these curves, guided by displays of the curve, its derivative, and its curvature. Then the curves are 59726SV_FM_FM pi-xxiii c< 11/22/08 3: 08 PM Page iii connected to each other by a parametric surface. The CAtia program was developed in france and again the architect can do so in many possible by Dassault Systemes, originally for designing ways with the guidance of displays of the geometric airplanes, and was subsequently employed in characteristics of the surface the automotive industry. Frank gehry, because of The Catia model is then used to produce his complex sculptural shapes, is the first to use another physical model, which, in turn, suggests it in architecture. It helps him answer his ques modifications and leads to additional computer tion,How wiggly can you get and still make a and physical models building? 59726SV_FM__ FM pi-xxiii cK< 11/ 22/08 3: 08 PM Page iv 59726SV_FM__ FM pi-xxiii cK< 11/ 22/08 3: 08 PM Page v Single Variable Calculus Concepts and Contexts 4e James stewart McMaster University University Toronto e BROOKS/COLE CENGAGE Learning Australia. Brazil Japan. Korea. Mexico. Singapore. Spain, United Kingdom. United States 59726SV_FM_ FM pi-xxiii cK< 11/22/08 3: 08 PM Page vi e BROOKS/COLE W CENGAGE Learning Single Variable Calculus: Concepts and Contexts, C)2010, 2005 Brooks/Cole, Cengage Learning Fourth edition 」 ames stewart ALL RIGHTS RESERVED. No part of this work covered by the copy right herein may be reproduced, transmitted, stored, or used in any Publisher: richard stratton form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, Senior Developmental Editor: Jay Campbell taping, Web distribution, information networks, or information Associate Editor: Jeannine Lawless storage and retrieval systems, except as permitted under Section Editorial assistant: Elizabeth Neustaetter 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. Media Editor: Peter galuardi Senior Marketing Manager: Jennifer Jones For product information and technology assistance, contact us at marketing Assistant: Angela Kim Cengage Learning Customer Sales Support, 1-800-354-9706 Marketing Communications Manager: Mary Anne Payumo For permission to use material from this text or product, Senior Project Manager, Editorial Production submitallrequestsonlineatwww.cengage.com/permissions. Cheryll Linthicum Further permissions questions can be e-mailed to permissionrequest@cengage.com. Creative Director: Rob hugel Senior art Director: Vernon boes Library of Congress Control Number 2008941253 Senior Print Buyer: Becky Cross SBN-13:978-0-495-55972-6 Permissions editor: Bob kauser SBN-10:0495559725 Production service: tECH arts Text Des g ner:」 anne Calabrese Photo Researcher: Pre-Press PMg Brooks/Cole 10 Davis Drive Copy Editor: Kathi Townes Belmont, CA 94002-3098 Illustrator: Brian Betsill Cover Designer: Irene Morris CoverImageandpageiv:thomasmayerarchive.com Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singa Compositor: Stephanie Kuhns, TECHarts pore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locateyourlocalofficeatwww.cengage.com/international Cengage Learning products are represented in Canada by Nelson education Ltd To learn more about brooks/ cole, visit www.cengage.com/brookscole Purchase any of our products at your local college store or at our preferredonlinestorewww.ichapters.com Trademarks Derive is a registered trademark of Soft Warehouse Ir Maple is a registered trademark of Waterloo Maple, Inc. Mathematica is a registered trademark of Wolfram Research, Inc Tools for Enriching is a trademark used herein under license Printed in Canada 12345671211100908 59726SV_FM__FM pi-xxiii c 11/ 22/08 3: 08 PM To li Li 【实例截图】
【核心代码】
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