Single Variable Calculus. Early Transcendentals, 7th Edition

✍ Scribed by James Stewart

• Publisher: Brooks Cole
• Year: 2011
• Tongue: English
• Leaves: 948
• Edition: 7th
• Category: Library

✦ Synopsis

Success in your calculus course starts here! James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With SINGLE VARIABLE CALCULUS: EARLY TRANSCENDENTALS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright......Page 6
Contents......Page 9
Preface......Page 15
To the Student......Page 26
Diagnostic Tests......Page 28
A PREVIEW OF CALCULUS......Page 33
1 Functions and Models......Page 41
1.1 Four Ways to Represent a Function......Page 42
Representations of Functions......Page 44
Piecewise Defined Functions......Page 48
Exercises......Page 51
Linear Models......Page 55
Polynomials......Page 59
Power Functions......Page 60
Algebraic Functions......Page 62
Trigonometric Functions......Page 63
Logarithmic Functions......Page 64
Exercises......Page 65
Transformations of Functions......Page 68
Combinations of Functions......Page 71
Exercises......Page 74
1.4 Graphing Calculators and Computers......Page 76
Exercises......Page 82
1.5 Exponential Functions......Page 83
Applications of Exponential Functions......Page 86
The Number......Page 87
Exercises......Page 89
1.6 Inverse Functions and Logarithms......Page 90
Logarithmic Functions......Page 94
Natural Logarithms......Page 96
Graph and Growth of the Natural Logarithm......Page 98
Inverse Trigonometric Functions......Page 99
Exercises......Page 101
Review......Page 104
Principles of Problem Solving......Page 107
2 Limits and Derivatives......Page 113
The Tangent Problem......Page 114
The Velocity Problem......Page 116
Exercises......Page 118
2.2 The Limit of a Function......Page 119
One-Sided Limits......Page 123
Infinite Limits......Page 125
Exercises......Page 128
2.3 Calculating Limits Using the Limit Laws......Page 131
Exercises......Page 138
2.4 The Precise Definition of a Limit......Page 140
Infinite Limits......Page 147
Exercises......Page 148
2.5 Continuity......Page 150
Exercises......Page 159
2.6 Limits at Infinity; Horizontal Asymptotes......Page 162
Infinite Limits at Infinity......Page 168
Precise Definitions......Page 169
Exercises......Page 172
Tangents......Page 175
Velocities......Page 177
Derivatives......Page 178
Rates of Change......Page 179
Exercises......Page 182
Writing Project: Early Methods for Finding Tangents......Page 185
2.8 The Derivative as a Function......Page 186
Other Notations......Page 189
How Can a Function Fail to Be Differentiable?......Page 191
Higher Derivatives......Page 192
Exercises......Page 194
Review......Page 197
Problems Plus......Page 202
3 Differentiation Rules......Page 205
Power Functions......Page 206
New Derivatives from Old......Page 209
Exponential Functions......Page 211
Exercises......Page 213
The Product Rule......Page 216
The Quotient Rule......Page 219
Exercises......Page 221
3.3 Derivatives of Trigonometric Functions......Page 223
Exercises......Page 229
3.4 The Chain Rule......Page 230
How to Prove the Chain Rule......Page 236
Exercises......Page 237
Applied Project: Where Should a Pilot Start Descent?......Page 240
3.5 Implicit Differentiation......Page 241
Derivatives of Inverse Trigonometric Functions......Page 245
Exercises......Page 247
Laboratory Project: Families of Implicit Curves......Page 249
3.6 Derivatives of Logarithmic Functions......Page 250
Logarithmic Differentiation......Page 252
The Number e as a Limit......Page 254
Exercises......Page 255
Physics......Page 256
Chemistry......Page 259
Biology......Page 261
Economics......Page 263
Other Sciences......Page 264
Exercises......Page 265
Population Growth......Page 269
Radioactive Decay......Page 271
Newton’s Law of Cooling......Page 272
Continuously Compounded Interest......Page 273
Exercises......Page 274
3.9 Related Rates......Page 276
Exercises......Page 280
3.10 Linear Approximations and Differentials......Page 282
Applications to Physics......Page 284
Differentials......Page 285
Exercises......Page 287
Laboratory Project: Taylor Polynomials......Page 288
3.11 Hyperbolic Functions......Page 289
Inverse Hyperbolic Functions......Page 292
Exercises......Page 294
Review......Page 296
Problems Plus......Page 300
4 Applications of Differentiation......Page 305
4.1 Maximum and Minimum Values......Page 306
Exercises......Page 312
Applied Project: The Calculus of Rainbows......Page 314
4.2 The Mean Value Theorem......Page 316
Exercises......Page 320
What Does f' Say About f?......Page 322
What Does f" Say About f?......Page 324
Exercises......Page 329
4.4 Indeterminate Forms and l’Hospital’s Rule......Page 333
Indeterminate Differences......Page 337
Indeterminate Powers......Page 338
4.5 Summary of Curve Sketching......Page 342
Guidelines for Sketching a Curve......Page 343
Slant Asymptotes......Page 347
4.6 Graphing with Calculus and Calculators......Page 350
Exercises......Page 356
4.7 Optimization Problems......Page 357
Applications to Business and Economics......Page 362
Exercises......Page 363
Applied Project: The Shape of a Can......Page 369
4.8 Newton’s Method......Page 370
Exercises......Page 374
4.9 Antiderivatives......Page 376
Rectilinear Motion......Page 379
Exercises......Page 380
Review......Page 383
Problems Plus......Page 387
5 Integrals......Page 391
5.1 Areas and Distances......Page 392
The Distance Problem......Page 399
Exercises......Page 401
5.2 The Definite Integral......Page 403
Evaluating Integrals......Page 406
The Midpoint Rule......Page 410
Properties of the Definite Integral......Page 411
Exercises......Page 414
Discovery Project: Area Functions......Page 417
5.3 The Fundamental Theorem of Calculus......Page 418
Differentiation and Integration as Inverse Processes......Page 425
Exercises......Page 426
Indefinite Integrals......Page 429
Applications......Page 432
Exercises......Page 435
Writing Project: Newton, Leibniz, and the Invention of Calculus......Page 438
5.5 The Substitution Rule......Page 439
Definite Integrals......Page 443
Symmetry......Page 444
Exercises......Page 445
Review......Page 447
Problems Plus......Page 451
6 Applications of Integration......Page 453
6.1 Areas Between Curves......Page 454
Exercises......Page 459
Applied Project: The Gini Index......Page 461
6.2 Volumes......Page 462
Exercises......Page 470
6.3 Volumes by Cylindrical Shells......Page 473
Exercises......Page 476
6.4 Work......Page 478
Exercises......Page 481
6.5 Average Value of a Function......Page 483
Exercises......Page 485
Applied Project: Calculus and Baseball......Page 487
Applied Project: Where to Sit at the Movies......Page 488
Review......Page 489
Problems Plus......Page 491
7 Techniques of Integration......Page 495
7.1 Integration by Parts......Page 496
Exercises......Page 500
7.2 Trigonometric Integrals......Page 503
Exercises......Page 508
7.3 Trigonometric Substitution......Page 510
Exercises......Page 515
7.4 Integration of Rational Functions by Partial Fractions......Page 516
Exercises......Page 524
7.5 Strategy for Integration......Page 526
Can We Integrate All Continuous Functions?......Page 530
Exercises......Page 531
Tables of Integrals......Page 532
Computer Algebra Systems......Page 534
Exercises......Page 536
Discovery Project: Patterns in Integrals......Page 537
7.7 Approximate Integration......Page 538
Simpson’s Rule......Page 543
Exercises......Page 548
Type 1: Infinite Intervals......Page 551
Type 2: Discontinuous Integrands......Page 555
A Comparison Test for Improper Integrals......Page 557
Exercises......Page 559
Review......Page 561
Problems Plus......Page 565
8 Further Applications of Integration......Page 569
8.1 Arc Length......Page 570
The Arc Length Function......Page 573
Exercises......Page 575
8.2 Area of a Surface of Revolution......Page 577
Exercises......Page 582
Discovery Project: Rotating on a Slant......Page 583
Hydrostatic Pressure and Force......Page 584
Moments and Centers of Mass......Page 586
Exercises......Page 592
Discovery Project: Complementary Coffee Cups......Page 594
Consumer Surplus......Page 595
Blood Flow......Page 596
Cardiac Output......Page 597
Exercises......Page 598
8.5 Probability......Page 600
Average Values......Page 602
Normal Distributions......Page 604
Exercises......Page 605
Review......Page 607
Problems Plus......Page 609
9 Differential Equations......Page 611
Models of Population Growth......Page 612
General Differential Equations......Page 614
Exercises......Page 616
Direction Fields......Page 617
Euler’s Method......Page 621
Exercises......Page 624
9.3 Separable Equations......Page 626
Orthogonal Trajectories......Page 629
Mixing Problems......Page 630
Exercises......Page 632
Applied Project: How Fast Does a Tank Drain?......Page 635
Applied Project: Which Is Faster, Going Up or Coming Down?......Page 636
The Law of Natural Growth......Page 637
The Logistic Model......Page 638
Comparison of the Natural Growth and Logistic Models......Page 642
Other Models for Population Growth......Page 644
Exercises......Page 645
9.5 Linear Equations......Page 648
Application to Electric Circuits......Page 651
Exercises......Page 652
9.6 Predator-Prey Systems......Page 654
Exercises......Page 659
Review......Page 661
Problems Plus......Page 665
10 Parametric Equations and Polar Coordinates......Page 667
10.1 Curves Defined by Parametric Equations......Page 668
Graphing Devices......Page 670
The Cycloid......Page 671
Families of Parametric Curves......Page 672
Exercises......Page 673
Laboratory Project: Running Circles around Circles......Page 676
Tangents......Page 677
Areas......Page 679
Arc Length......Page 680
Surface Area......Page 682
Exercises......Page 683
Laboratory Project: Bézier Curves......Page 685
10.3 Polar Coordinates......Page 686
Polar Curves......Page 688
Tangents to Polar Curves......Page 691
Graphing Polar Curves with Graphing Devices......Page 693
Exercises......Page 694
Laboratory Project: Families of Polar Curves......Page 696
10.4 Areas and Lengths in Polar Coordinates......Page 699
Exercises......Page 700
Parabolas......Page 702
Ellipses......Page 704
Hyperbolas......Page 705
Shifted Conics......Page 707
Exercises......Page 708
10.6 Conic Sections in Polar Coordinates......Page 710
Kepler’s Laws......Page 714
Exercises......Page 716
Review......Page 717
Problems Plus......Page 720
11 Infinite Sequences and Series......Page 721
11.1 Sequences......Page 722
Exercises......Page 732
11.2 Series......Page 735
Exercises......Page 743
11.3 The Integral Test and Estimates of Sums......Page 746
Estimating the Sum of a Series......Page 750
Exercises......Page 752
11.4 The Comparison Tests......Page 754
Estimating Sums......Page 757
Exercises......Page 758
11.5 Alternating Series......Page 759
Estimating Sums......Page 762
Exercises......Page 763
11.6 Absolute Convergence and the Ratio and Root Tests......Page 764
Exercises......Page 769
11.7 Strategy for Testing Series......Page 771
Exercises......Page 772
11.8 Power Series......Page 773
Exercises......Page 777
11.9 Representations of Functions as Power Series......Page 778
Differentiation and Integration of Power Series......Page 780
Exercises......Page 783
11.10 Taylor and Maclaurin Series......Page 785
Multiplication and Division of Power Series......Page 795
Exercises......Page 797
Writing Project: How Newton Discovered the Binomial Series......Page 799
Approximating Functions by Polynomials......Page 800
Applications to Physics......Page 804
Exercises......Page 806
Applied Project: Radiation from the Stars......Page 809
Review......Page 810
Problems Plus......Page 813
Appendixes......Page 817
A: Numbers, Inequalities, and Absolute Values......Page 818
B: Coordinate Geometry and Lines......Page 826
C: Graphs of Second-Degree Equations......Page 832
D: Trigonometry......Page 840
E: Sigma Notation......Page 850
F: Proofs of Theorems......Page 855
G: The Logarithm Defined as an Integral......Page 864
H: Complex Numbers......Page 871
I: Answers to Odd-Numbered Exercises......Page 879
Index......Page 931