This manual includes worked-out solutions to every odd-numbered exercise in Single Variable Calculus, 7e (Chapters 1-11 of Calculus, 7e).
The Study Guide is also valuable in terms of practice and feedback. The philosophy of the Stewart sequence is, I believe, to combine theory, proofs along with applications and problem-solving. The feedback in the Student Solutions and the Study Guide provides a way to keep the student moving in the right direction.
Author(s): James Stewart
Edition: 7
Publisher: Cengage Learning
Year: 2011
Language: English
Pages: 579
Front Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Preface......Page 4
Abbreviations and Symbols......Page 5
CONTENTS......Page 7
Test A: Algebra......Page 13
Test B: Analytic Geometry......Page 15
Test C: Functions......Page 17
Test D: Trigonometry......Page 19
1.1 Four Ways to Represent a Function......Page 21
1.2 Mathematical Models: A Catalog of Essential Functions......Page 26
1.3 New Functions from Old Functions......Page 30
1.4 The Tangent and Velocity Problems......Page 36
1.5 The Limit of a Function......Page 38
1.6 Calculating Limits Using the Limit Laws......Page 41
1.7 The Precise Definition of a Limit......Page 46
1.8 Continuity......Page 50
1 Review......Page 55
Principles of Problem Solving......Page 63
2.1 Derivatives and Rates of Change......Page 65
2.2 The Derivative as a Function......Page 70
2.3 Differentiation Formulas......Page 76
2.4 Derivatives of Trigonometric Functions......Page 83
2.5 The Chain Rule......Page 86
2.6 Implicit Differentiation......Page 91
2.7 Rates of Change in the Natural and Social Sciences......Page 97
2.8 Related Rates......Page 101
2.9 Linear Approximations and Differentials......Page 106
2 Review......Page 109
Problems Plus......Page 117
3.1 Maximum and Minimum Values......Page 123
3.2 The Mean Value Theorem......Page 128
3.3 How Derivatives Affect the Shape of a Graph......Page 130
3.4 Limits at Infinity; Horizontal Asymptotes......Page 140
3.5 Summary of Curve Sketching......Page 147
3.6 Graphing with Calculus and Calculators......Page 156
3.7 Optimization Problems......Page 164
3.8 Newton's Method......Page 174
3.9 Antiderivatives......Page 179
3 Review......Page 184
Problems Plus......Page 195
4.1 Areas and Distances......Page 201
4.2 The Definite Integral......Page 206
4.3 The Fundamental Theorem of Calculus......Page 211
4.4 Indefinite Integrals and the Net Change Theorem......Page 217
4.5 The Substitution Rule......Page 220
4 Review......Page 224
Problems Plus......Page 229
5.1 Areas Between Curves......Page 231
5.2 Volumes......Page 238
5.3 Volumes by Cylindrical Shells......Page 246
5.4 Work......Page 250
5.5 Average Value of a Function......Page 253
5 Review......Page 254
Problems Plus......Page 259
6.1 Inverse Functions......Page 263
6.2 Exponential Functions and Their Derivatives......Page 266
6.3 Logarithmic Functions......Page 273
6.4 Derivatives of Logarithmic Functions......Page 276
6.2* The Natural Logarithmic Function......Page 282
6.3* The Natural Exponential Function......Page 289
6.4* General Logarithmic and Exponential Functions......Page 295
6.5 Exponential Growth and Decay......Page 298
6.6 Inverse Trigonometric Functions......Page 300
6.7 Hyperbolic Functions......Page 306
6.8 Indeterminate Forms and l'Hospital's Rule......Page 310
6 Review......Page 318
Problems Plus......Page 327
7.1 Integration by Parts......Page 331
7.2 Trigonometric Integrals......Page 337
7.3 Trigonometric Substitution......Page 341
7.4 Integration of Rational Functions by Partial Fractions......Page 346
7.5 Strategy for Integration......Page 355
7.6 Integration Using Tables and Computer Algebra Systems......Page 361
7.7 Approximate Integration......Page 365
7.8 Improper Integrals......Page 373
7 Review......Page 380
Problems Plus......Page 387
8.1 Arc Length......Page 391
8.2 Area of a Surface of Revolution......Page 394
8.3 Applications to Physics and Engineering......Page 398
8.4 Applications to Economics and Biology......Page 405
8.5 Probability......Page 406
8 Review......Page 409
Problems Plus......Page 413
9.1 Modeling with Differential Equations......Page 417
9.2 Direction Fields and Euler's Method......Page 418
9.3 Separable Equations......Page 423
9.4 Models for Population Growth......Page 429
9.5 Linear Equations......Page 433
9.6 Predator-Prey Systems......Page 437
9 Review......Page 439
Problems Plus......Page 445
10.1 Curves Defined by Parametric Equations......Page 449
10.2 Calculus with Parametric Curves......Page 455
10.3 Polar Coordinates......Page 461
10.4 Areas and Lengths in Polar Coordinates......Page 468
10.5 Conic Sections......Page 474
10.6 Conic Sections in Polar Coordinates......Page 480
10 Review......Page 483
Problems Plus......Page 491
11.1 Sequences......Page 493
11.2 Series......Page 499
11.3 The Integral Test and Estimates of Sums......Page 507
11.4 The Comparison Tests......Page 510
11.5 Alternating Series......Page 513
11.6 Absolute Convergence and the Ratio and Root Tests......Page 516
11.7 Strategy for Testing Series......Page 520
11.8 Power Series......Page 522
11.9 Representations of Functions as Power Series......Page 526
11.10 Taylor and Maclaurin Series......Page 531
11.11 Applications of Taylor Polynomials......Page 538
11 Review......Page 545
Problems Plus......Page 553
A: Numbers, Inequalities, and Absolute Values......Page 559
B: Coordinate Geometry and Lines......Page 561
C: Graphs of Second-Degree Equations......Page 564
D: Trigonometry......Page 566
E: Sigma Notation......Page 570
G: Graphing Calculators and Computers......Page 573
H: Complex Numbers......Page 576
