应用微积分（英文版·原书第5版）

.2.6 the derivative 155
using technology: graphing a function and its tangent lines 176
chapter 2 summary of principal formulas and terms 179
chapter 2 review exercises 179
chapter 3 differentiation 182
3.1 basic rules of differentiation 184
using technology: finding the rate of change of a function 192
3.2 the product and quotient rules 198
using technology: the product and quotient rules 208
3.3 the chain rule 211
using technology: finding the derivative of a
composite function 218
* sections marked with an asterisk are not prerequisites for later material.
3.4 marginal functions in economics 224
3.5 higher-order derivatives 240
using technology: finding the second derivative of a function at a
given point 246
*3.6 implicit differentiation and related rates 249
3.7 differentials 261
portfolio: john decker 262
using technology: finding the differential of a function 270
chapter 3 summary of principal formulas and terms 273
chapter 3 review exercises 274
chapter 4 applications of the derivative 276
4.1 applications of the first derivative 278
using technology: using the first derivative to analyze
a function 296
4.2 applications of the second derivative 301
using technology: finding the inflection points of a function 318
4.3 curve sketching 321
using technology: analyzing the properties of a function 334
4.4 optimization i 341
using technology: finding the absolute extrema of a function 354
4.5 optimization ii 357
chapter 4 summary of principal terms 369
chapter 4 review exercises 369
chapter 5 exponential and logarithmic functions 372
5.1 exponential functions 374
using technology 380
5.2 logarithmic functions 383
5.3 compound interest 391
portfolio: misato nakazaki 403
5.4 differentiation of exponential functions 405
using technology 414
5.5 differentiation of logarithmic functions 417
*5.6 exponential functions as mathematical models 425
chapter 5 summary of principal formulas and terms 436
chapter 5 review exercises 437
chapter 6 integration 438
6.1 antiderivatives and the rules of integration 440
6.2 integration by substitution 455
6.3 area and the definite integral 466
6.4 the fundamental theorem of calculus 477
using technology: evaluating definite integrals 488
6.5 evaluating definite integrals 491
using technology: evaluating definite integrals for
piecewise-defined functions 500
6.6 area between two curves 503
using technology: finding the area between two curves 516
*6.7 applications of the definite integral to business
and economics 519
using technology: consumers' surplus and producers' surplus 533
*6.8 volumes of solids of revolution 535
chapter 6 summary of principal formulas and terms 543
chapter 6 review exercises 544
chapter 7 additional topics in integration 548
7.1 integration by parts 550
*7.2 integration using tables of integrals 557
*7.3 numerical integration 565
portfolio: james h. chesebro, m.d. 580
7.4 improper integrals 582
chapter 7 summary of principal formulas and terms 593
chapter 7 review exercises 594
chapter 8 calculus of several variables 596
8.1 functions of several variables 598
8.2 partial derivatives 608
using technology: finding partial derivatives at a given point 622
8.3 maxima and minima of functions of several variables 626
8.4 the method of least squares 637
using technology: finding an equation of a least-squares line 646
8.5 constrained maxima and minima and the method of
lagrange multipliers 650
*8.6 total differentials 663
*8.7 double integrals 669
*8.8 applications of double integrals 677
chapter 8 summary of principal terms 687
chapter 8 review exercises 687
chapter 9 differential equations 690
9.1 differential equations 692
9.2 separation of variables 699
9.3 applications of separable differential equations 706
9.4 approximate solutions of differential equations 716
chapter 9 summary of principal terms 724
chapter 9 review exercises 724
chapter 10 probability and calculus 726
10.1 probability distributions of random variables 728
using technology: graphing a histogram 736
10.2 expected value and standard deviation 739
using technology: finding the mean and standard deviation 754
10.3 normal distributions 756
chapter 10 summary of principal formulas and terms 769
chapter 10 review exercises 770
chapter 11 taylor polynomials and infinite series 772
11.1 taylor polynomials 774
11.2 infinite sequences 787
11.3 infinite series 796
11.4 series with positive terms 808
11.5 power series and taylor series 819
11.6 more on taylor series 829
*11.7 the newton-raphson method 839
chapter 11 summary of principal formulas and terms 849
chapter 11 review exercises 850
chapter 12 trigonometric functions 852
12.1 measurement of angles 854
12.2 the trigonometric functions 860
12.3 differentiation of trigonometric functions 871
using technology: analyzing trigonometric functions 884
12.4 integration of trigonometric functions 887
using technology: evaluating integrals of
trigonometric functions 892
chapter 12 summary of principal formulas and terms 896
chapter 12 review exercises 897
table 899
the standard normal distribution 900
answers to odd-numbered exercises 903
index 945
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