INSTRUCTOR S RESOURCE GUIDE AND TEST BANK

1 Download instant at Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo INSTRUCTOR S RESOURCE GUIDE AND TEST BANK BERNARD GILLETT University of Colorado Boulder CALCULUS FOR SCIENTISTS AND ENGINEERS EARLY TRANSCENDENTALS William Briggs University of Colorado Denver Lyle Cochran Whitworth University Bernard Gillett University of Colorado Boulder with the assistance of Eric Schulz Walla Walla Community College download instant at The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book.

2 The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Reproduced by Pearson from electronic files supplied by the author. Copyright 2013 Pearson Education, Inc. Publishing as Pearson, 75 Arlington Street, Boston, MA 02116. 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 the prior written permission of the publisher. Printed in the United States of America. ISBN-13: 978-0-321-78538-1 ISBN-10: 0-321-78538-X 1 2 3 4 5 6 OPM 16 15 14 13 12 download instant at Copyright 2013 Pearson Education, Inc. iiiTable of Contents Preface viii Learning Objectives xii Index of Applications xxxi Chapter 1 Functions 1 Review of Functions 1 Representing Functions 4 Inverse, Exponential.

3 And Logarithmic Functions 8 Trigonometric Functions and Their Inverses 11 Chapter 1 Key Terms and Concepts 14 Chapter 1 Review Questions 15 Chapter 1 Test Bank Exercises 16 Chapter 2 Limits 19 The Idea of Limits 19 Definitions of Limits 22 Techniques for Computing Limits 25 Infinite Limits 28 Limits at Infinity 31 Continuity 34 Precise Definitions of Limits 37 Chapter 2 Key Terms and Concepts 39 Chapter 2 Review Questions 40 Chapter 2 Test Bank Exercises 41 Chapter 3 Derivatives 43 Introducing the Derivative 43 Rules of Differentiation 46 The Product and Quotient Rules 49 Derivatives of Trigonometric Functions 52 Derivatives as Rates of Change 54 The Chain Rule 56 Implicit Differentiation 59 Derivatives of Logarithmic and Exponential Functions 62 Derivatives of Inverse Trigonometric Functions 64 Related Rates 67 Chapter 3 Key Terms and Concepts 69 Chapter 3 Review Questions 70 Chapter 3 Test Bank Exercises 72 download instant at Copyright 2013 Pearson Education, Inc.

4 Iv Chapter 4 Applications of the Derivative 75 Maxima and Minima 75 What Derivatives Tell Us 78 Graphing Functions 81 Optimization Problems 84 Linear Approximation and Differentials 86 Mean Value Theorem 89 L H pital s Rule 92 Newton s Method 95 Antiderivatives 99 Chapter 4 Key Terms and Concepts 101 Chapter 4 Review Questions 102 Chapter 4 Test Bank Exercises 103 Chapter 5 Integration 105 Approximating Areas under Curves 105 Definite Integrals 108 Fundamental Theorem of Calculus 111 Working with Integrals 114 Substitution Rule 116 Chapter 5 Key Terms and Concepts 118 Chapter 5 Review Questions 119 Chapter 5 Test Bank Exercises 120 Chapter 6 Applications of Integration 123 Velocity and Net Change 123 Regions Between Curves 128 Volume by Slicing 131 Volume by Shells 134 Length of Curves 136 Surface Area 138 Physical Applications 142 Logarithmic and Exponential Functions Revisited 145 Exponential Models 147 Hyperbolic Functions 149 Chapter 6 Key Terms and Concepts 153 Chapter 6 Review Questions 154 Chapter 6 Test Bank Exercises 156 Chapter 7 Integration Techniques 161 Basic Approaches 161 Integration by Parts 165 Trigonometric Integrals 169 Trigonometric Substitutions 172 Partial Fractions 175 Other Integration Strategies 177 Numerical Integration 179 Improper Integrals 181 Chapter 7 Key Terms and Concepts 183 Chapter 7 Review Questions 184 Chapter 7 Test Bank Exercises 185 download instant at Copyright 2013 Pearson Education, Inc.

5 VChapter 8 Differential Equations 187 Basic Ideas 187 Direction Fields and Euler s Method 191 Separable Differential Equations 194 Special First-Order Linear Differential Equations 196 Modeling with Differential Equations 198 Chapter 8 Key Terms and Concepts 200 Chapter 8 Review Questions 201 Chapter 8 Test Bank Exercises 203 Chapter 9 Sequences and Infinite Series 205 An Overview 205 Sequences 208 Infinite Series 210 The Divergence and Integral Tests 212 The Ratio, Root, and Comparison Tests 214 Alternating Series 217 Chapter 9 Key Terms and Concepts 219 Chapter 9 Review Questions 220 Chapter 9 Test Bank Exercises 222 Chapter 10 Power Series 223 Approximating Functions with Polynomials 223 Properties of Power Series 226 Taylor Series 228 Working with Taylor Series 230 Chapter 10 Key Terms and Concepts 232 Chapter 10 Review Questions 233 Chapter 10 Test Bank Exercises 234 Chapter 11 Parametric and Polar Curves 237 Parametric Equations 237 Polar Coordinates 240 Calculus in Polar Coordinates 243 Conic Sections 246 Chapter 11 Key Terms and Concepts 249 Chapter 11 Review Questions 250 Chapter 11 Test Bank Exercises 251 Chapter 12 Vectors and Vector-Valued Functions 253 Vectors in the Plane 254 Vectors in Three Dimensions 257 Dot Products 260 Cross Products 262 Lines and Curves in Space

6 264 Calculus of Vector-Valued Functions 267 Motion in Space 269 Length of Curves 271 Curvature and Normal Vectors 273 Chapter 12 Key Terms and Concepts 276 Chapter 12 Review Questions 277 Chapter 12 Test Bank Exercises 279 download instant at Copyright 2013 Pearson Education, Inc. vi Chapter 13 Functions of Several Variables 281 Planes and Surfaces 281 Graphs and Level Curves 284 Limits and Continuity 287 Partial Derivatives 290 The Chain Rule 292 Directional Derivatives and the Gradient 294 Tangent Planes and Linear Approximation 297 Maximum/Minimum Problems 299 Lagrange Multipliers 301 Chapter 13 Key Terms and Concepts 304 Chapter 13 Review Questions 305 Chapter 13 Test Bank Exercises 307 Chapter 14 Multiple Integration 311 Double Integrals over Rectangular Regions 311 Double Integrals over General Regions 314 Double Integrals in Polar Coordinates 317 Triple Integrals 319 Triple Integrals in Cylindrical and Spherical Coordinates 322 Integrals for Mass Calculations 326 Change of Variables in Multiple Integrals 328 Chapter 14 Key Terms and Concepts 330 Chapter 14 Review Questions 331 Chapter 14 Test

7 Bank Exercises 333 Chapter 15 Vector Calculus 337 Vector Fields 337 Line Integrals 341 Conservative Vector Fields 344 Green s Theorem 346 Divergence and Curl 348 Surface Integrals 350 Stokes Theorem 353 Divergence Theorem 355 Chapter 15 Key Terms and Concepts 357 Chapter 15 Review Questions 358 Chapter 15 Test Bank Exercises 359 download instant at Copyright 2013 Pearson Education, Inc. viiChapter 1 Guided Projects 1. Problem-solving skills 361 2. Constant-rate problems 364 3. Functions in action I 366 4. Functions in action II 368 5. Supply and demand 370 6. Phase and amplitude 373 7. Atmospheric CO2 375 8. Acid, noise, and earthquakes 376 Chapter 2 Guided Projects 9. Fixed point iteration 378 10. Local linearity 380 Chapter 3 Guided Projects 11. Numerical differentiation 382 12. Enzyme kinetics 384 13. Elasticity in economics 386 14.

8 Pharmacokinetics drug metabolism 388 Chapter 4 Guided Projects 15. Oscillators 389 16. Ice cream, geometry and calculus 391 17. Newton s method 393 Chapter 5 Guided Projects 18. Limits of sums 396 19. Distribution of wealth 397 20. Symmetry in integrals 399 Chapter 6 Guided Projects 21. Means and tangent lines 400 22. Landing an airliner 402 23. Geometric probability 404 24. Mathematics of the CD player 407 25. Designing a water clock 409 26. Buoyancy and Archimedes principle 411 27. Dipstick problems 413 28. Hyperbolic functions 416 29. Optimizing fuel use 418 30. Inverse sine from geometry 420 Chapter 7 Guided Projects 31. Simpson s rule 422 32. How long will your iPod last? 425 33. Mercator projections 427 Chapter 8 Guided Projects 34. Cooling coffee 430 35. Euler s method for differential equations 432 36. Predator-prey models 435 37. Period of the pendulum 439 38. Terminal velocity 442 39.

9 Logistic growth 445 40. A pursuit problem 448 Chapter 9 Guided Projects 41. Chaos! 450 42. Financial matters 452 43. Periodic drug dosing 455 44. Economic stimulus packages 457 45. The mathematics of loans 459 46. Archimedes approximation to 460 47. Exact values of infinite series 462 48. Conditional convergence in a crystal lattice 464 Chapter 10 Guided Projects 49. Series approximations to 466 50. Euler s formula (Taylor series with complex numbers) 468 51. Stirling s formula and n! 469 52. Three-sigma quality control 471 53. Fourier series 474 Chapter 11 Guided Projects 54. The amazing cycloid 480 55. Parametric art 483 56. Polar art 488 57. Grazing goat problems 491 58. Translations and rotations of axes 494 59. Celestial orbits 498 60. Properties of conic sections 500 Chapter 12 Guided Projects 61. Designing a trajectory 504 62. Intercepting a UFO 507 63. CORDIC algorithms: How your calculator works 509 64.

10 Bezier curves for graphic design 514 65. Kepler s laws 516 Chapter 13 Guided Projects 66. Traveling waves 519 67. Ecological diversity 522 68. Economic production functions 524 Chapter 14 Guided Projects 69. How big are n-balls? 527 70. Electric field integrals 529 71. The tilted cylinder problem 533 72. The exponential Eiffel Tower 535 73. Moments of inertia 537 74. Gravitational fields 540 Chapter 15 Guided Projects 75. Ideal fluid flow 543 76. Maxwell s equations 546 77. Planimeters and vector fields 552 78. Vector calculus in other coordinate systems 555 Answers to Chapter-Level Content A-1 Solutions to Guided Projects A-68 Single Variable Student Study Cards SC-1 Multivariable Student Study Cards SC-8 download instant at Copyright 2013 Pearson Education, Inc. viii Preface This GUIDE accompanies Calculus for Scientists and Engineers: Early Transcendentals by Briggs, Cochran, Gillett, and Schulz.