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| 《微积分》（下）（第5版影印版）适于国内高等院校工科各专业和广大非数学专业（含文科、经管专业）本、专科生作为双语教学的教材使用。 |
| Preface xiv To the Student xxvi A Preview of Calculus 2 1 Functions and Hodels 10 1.1 Four Ways to Represent a Function 11 1.2 Mathematical Models: A Catalog of Essential Functions 25 i.3 New Functions from Old Functions 38 1.4 Graphing Calculators and Computers 48 1.5 Exponential Functions 55 1.6 Inverse Functions and Logarithms 63 Review 77 Principles of Problem Solving 80 2 Limils and Derivatives 8G 2.1 The Tangent and Velocity Problems 87 2.2 The Limit of a Function 92 2.3 Calculating Limits Using the Limit Laws 104 2.4 The Precise Definition of a Limit 114 2.5 Continuity 124 2.6 Limits at Infinity; Horizontal Asymptotes 135 2.7 Tangents， Velocities， and Other Rates of Change 149 2.8 Derivatives 158 Writing Project o Early Methods for Finding Tangents 164 2.9 The Derivative as a Function 165 Review 176 Problems Plus 180 3 Lifferenliatiun Rules 182 3.1 Derivatives of Polynomials and Exponential Functions 183 3.2 The Product and Quotient Rules 192 3.3 Rates of Change in the Natural and Social Sciences 199 3.4 Derivatives of Trigonometric Functions 211 3.5 The Chain Rule 217 3.6 Implicit Differentiation 227 3.7 Higher Derivatives 236 Applied Project o Where Should a Pilot Start Descent? 243 Applied Project o Building a Better Roller Coaster 243 3.8 Derivatives of Logarithmic Functions 244 3.9 Hyperbolic Functions 250 3.10 Related Rates 256 3.11 Linear Approximations and Differentials 262 Laboratory Project o Taylor Polynomials 269 Review 270 Problems Plus 274 4 Applications of gifferenliulion 278 4.1 Maximum and Minimum Values 279 Applied Project o The Calculus of Rainbows 288 4.2 The Mean Value Theorem 290 4.3 How Derivatives Affect the Shape of a Graph 296 4.4 Indeterminate Forms and LHospitals Rule 307 Writing Project o The Origins of LHospitars Rule 315 4.5 Summary of Curve Sketching 316 4.6 Graphing with Calculus and Calculators 324 4.7 Optimization Problems 331 Applied Project o The Shape of a Can 341 4.8 Applications to Business and Economics 342 4.9 Newtons Method 347 4.10 Antiderivatives 353 Review 361 Problems Plus 365 5 Inteorals 360 5.1 Areas and Distances 369 5.2 The Definite Integral 380 Discovery Project o Area Functions 393 5.3 The Fundamental Theorem of Calculus 394 5.4 Indefinite Integrals and the Net Change Theorem 405 Writing Project o Newton， keibniz， and the Invention of Calculus 413 5.5 The Substitution Rule 414 5.6 The Logarithm Defined as an Integral 422 Review 430 Problems Plus 434 6 Applicotions of Inteoration 436 6.1 Areas between Curves 437 6.2 Volumes 444 6.3 Volumes by Cylindrical Shells 455 6.4 Work 460 6.5 Average Value of a Function 464 Applied Project o Where to Sit at the Movies 468 Review 468 Problems Plus 470 7 Techniques of Integration 474 7.1 Integration by Parts 475 7.2 Trigonometric Integrals 482 7.3 Trigonometric Substitution 489 7.4 Integration of Rational Functions by Partial Fractions 496 7.5 Strategy for Integration 505 7.6 Integration Using Tables and Computer Algebra Systems 511 Discovery Project o Patterns in Integrals 517 7.7 Approximate Integration 518 7.8 Improper Integrals 530 Review 540 Problems Plus 543 8 Further Applications of Inteoralion 546 8.1 Arc Length 547 Discovery Project o Arc Length Contest 554 8.2 Area of a Surface of Revolution 554 Discovery Project o Rotating on a Slant 560 8.3 Applications to Physics and Engineering 561 8.4 Applications to Economics and Biology 571 8.5 Probability 575 Review 582 Problems Plus 584 9 Diffeiential Equations 586 9.1 Modeling with Differential Equations 587 9.2 Direction Fields and Eulers Method 592 9.3 Separable Equations 601 Applied Project How Fast Does a Tank Drain? 609 Applied Project Which Is Faster， Going Up or Coming Down? 610 9.4 Exponential Growth and Decay 611 Applied Project Calculus and Baseball 622 …… 10 Parametric Equations and Polar Coordinates 11 Infinite Sequences and Series 12 Vectors and the Geometru of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus 17 Second-Order Offerential Equations Appendixes Index |
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