Stewart Calculus, 7th Edition

Stewart Calculus, 7th Edition Stewart Calculus, 7th Edition

ISBN: 9780538497817 / 0538497815

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Table of Contents

Chapter 1

Functions And Limits

1.1 Four Ways to Represent a Function Exercises p.19
1.2 Mathematical Models: A Catalog of Essential Functions Exercises p.33
1.3 New Functions from Old Functions Exercises p.42
1.4 The Tangent and Velocity Problems Exercises p.49
1.5 The Limit of a Function Exercises p.59
1.6 Calculating Limits Using the Limit Laws Exercises p.69
1.7 The Precise Definition of a Limit Exercises p.80
1.8 Continuity Exercises p.90
Concept Check p.93
True-False Quiz p.94
Review Exercises p.95
Problem Solving p.102

Chapter 2


2.1 Derivatives and Rates of Change Exercises p.110
2.2 The Derivative as a Function Exercises p.122
2.3 Differentiation Formulas Exercises p.136
2.4 Derivatives of Trigonometric Functions Exercises p.146
2.5 The Chain Rule Exercises p.154
2.6 Implicit Differentiation Exercises p.161
2.7 Rates of Change in the Natural and Social Sciences Exercises p.173
2.8 Related Rates Exercises p.180
2.9 Linear Approximations and Differentials Exercises p.187
Concept Check p.190
True-False Quiz p.190
Review Exercises p.191
Problems Plus p.194

Chapter 3

Applications Of Differentiation

3.1 Maximum and Minimum Values Exercises p.204
3.2 The Mean Value Theorem Exercises p.212
3.3 How Derivatives Affect the Shape of a Graph Exercises p.220
3.4 Limits at Infinity; Horizontal Asymptotes Exercises p.234
3.5 Summary of Curve Sketching Exercises p.242
3.6 Graphing with Calculus and Calculators Exercises p.249
3.7 Optimization Problems Exercises p.256
3.8 Newton's Method Exercises p.267
3.9 Antiderivatives Exercises p.273
Concept Check p.275
True-False Quiz p.276
Review Exercises p.276
Problem Solving p.280

Chapter 4


4.1 Areas and Distances Exercises p.293
4.2 The Definite Integral Exercises p.306
4.3 The Fundamental Theorem of Calculus Exercises p.318
4.4 Indefinite Integrals and the Net Change Theorem Exercises p.326
4.5 The Substitution Rule Exercises p.335
Concept Check p.337
True-False Quiz p.338
Review Exercises p.338
Problems Plus p.342

Chapter 5

Applications Of Integration

5.1 Areas Between Curves Exercises p.349
5.2 Volumes Exercises p.360
5.3 Volumes by Cylindrical Shells Exercises p.366
5.4 Work Exercises p.371
5.5 Average Value of a Function Exercises p.375
Concept Check p.377
Review Exercises p.378
Problems Plus p.380

Chapter 6

Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric …

6.1 Inverse Functions Exercises p.390
6.2 Exponential Functions and Their Derivatives Exercises p.401
6.3 Logarithmic Functions Exercises p.408
6.4 Derivatives of Logarithmic Functions Exercises p.418
6.2* The Natural Logarithmic Function Exercises p.428
6.3* The Natural Exponential Function Exercises p.434
6.4* General Logarithmic and Exponential Functions Exercises p.444
6.5 Exponential Growth and Decay Exercises p.451
6.6 Inverse Trigonometric Functions Exercises p.459
6.7 Hyperbolic Functions Exercises p.467
6.8 Indeterminate Forms and l'Hospital's Rule Exercises p.477
Concept Check p.480
True-False Quiz p.481
Review Exercises p.481
Problems Plus p.486

Chapter 7

Techniques Of Integration

7.1 Integration by Parts Exercises p.492
7.2 Trigonometric Integrals Exercises p.500
7.3 Trigonometric Substitution Exercises p.507
7.4 Integration of Rational Functions by Partial Fractions Exercises p.516
7.5 Strategy for Integration Exercises p.523
7.6 Integration Using Tables and Computer Algebra Systems Exercises p.528
7.7 Approximate Integration Exercises p.540
7.8 Improper Integrals Exercises p.551
Concept Check p.553
True-False Quiz p.554
Review Exercises p.554
Problems Plus p.558

Chapter 8

Further Applications Of Integration

8.1 Arc Length Exercises p.567
8.2 Area of a Surface of Revolution Exercises p.574
8.3 Applications to Physics and Engineering Exercises p.584
8.4 Applications to Economics and Biology Exercises p.590
8.5 Probability Exercises p.597
Concept Check p.599
Review Exercises p.599
Problems Plus p.601

Chapter 9

Differential Equations

9.1 Modeling with Differential Equations Exercises p.608
9.2 Direction FIelds and Euler's Method Exercises p.616
9.3 Separable Equations Exercises p.624
9.4 Models for Population Growth Exercises p.637
9.5 Linear Equations Exercises p.644
9.6 Predator-Prey Systems Exercises p.651
Concept Check p.653
True-False Quiz p.653
Review Exercises p.654
Problems Plus p.657

Chapter 10

Parametric Equations And Polar Coordinates

10.1 Curves Defined by Parametric Equations Exercises p.665
10.2 Calculus with Parametric Curves Exercises p.675
10.3 Polar Coordinates Exercises p.686
10.4 Areas and Lengths in Polar Coordinates Exercises p.692
10.5 Conic Sections Exercises p.700
10.6 Conic Sections in Polar Coordinates Exercises p.708
Concept Check p.709
True-False Quiz p.709
Review Exercises p.710
Problems Plus p.712

Chapter 11

Infinite Sequences And Series

11.1 Sequences Exercises p.724
11.2 Series Exercises p.735
11.3 The Integral Test and Estimates of Sums Exercises p.744
11.4 The Comparison Tests Exercises p.750
11.5 Alternating Series Exercises p.755
11.6 Absolute Convergence and the Ratio and Root Tests Exercises p.761
11.7 Strategy for Testing Series Exercises p.764
11.8 Power Series Exercises p.769
11.9 Representations of Functions as Power Series Exercises p.775
11.10 Taylor and Maclaurin Series Exercises p.789
11.11 Applications of Taylor Polynomials Exercises p.798
Concept Check p.802
True-False Quiz p.802
Review Exercises p.803
Problems Plus p.805

Chapter 12

Vectors And The Geometry Of Space

12.1 Three-Dimensional Coordinate Systems Exercises p.814
12.2 Vectors Exercises p.822
12.3 The Dot Product Exercises p.830
12.4 The Cross Product Exercises p.838
12.5 Equations of Lines and Planes Exercises p.848
12.6 Cylinders and Quadric Surfaces Exercises p.856
Concept Check p.858
True-False Quiz p.858
Review Exercises p.859
Problems Plus p.861

Chapter 13

Vector Functions

13.1 Vector Functions and Space Curves Exercises p.869
13.2 Derivatives and Integrals of Vector Functions Exercises p.876
13.3 Arc Length and Curvature Exercises p.884
13.4 Motion in Space: Velocity and Acceleration Exercises p.894
Concept Check p.897
True-False Quiz p.897
Review Exercises p.898
Problems Plus p.900

Chapter 14

Partial Derivatives

14.1 Functions of Several Variables Exercises p.912
14.2 Limits and Continuity Exercises p.923
14.3 Partial Derivatives Exercises p.935
14.4 Tangent Planes and Linear Approximations Exercises p.946
14.5 The Chain Rule Exercises p.954
14.6 Directional Derivatives and the Gradient Vector Exercises p.967
14.7 Maximum and Minimum Values Exercises p.977
14.8 Lagrange Multipliers Exercises p.987
Concept Check p.991
True-False Quiz p.991
Review Exercises p.992
Problems Plus p.995

Chapter 15

Multiple Integrals

15.1 Double Integrals over Rectangles Exercises p.1005
15.2 Iterated Integrals Exercises p.1011
15.3 Double Integrals over General Regions Exercises p.1019
15.4 Double Integrals in Polar Coordinates Exercises p.1026
15.5 Applications of Double Integrals Exercises p.1036
15.6 Surface Area Exercises p.1040
15.7 Triple Integrals Exercises p.1049
15.8 Triple Integrals in Cylindrical Coordinates Exercises p.1055
15.9 Triple Integrals in Spherical Coordinates Exercises p.1061
15.10 Change of Variables in Multiple Integrals Exercises p.1071
Concept Check p.1073
True-False Quiz p.1073
Review Exercises p.1074
Problems Plus p.1077

Chapter 16

Vector Calculus

16.1 Vector Fields Exercises p.1085
16.2 Line Integrals Exercises p.1096
16.3 The Fundamental Theorem for Line Integrals Exercises p.1106
16.4 Green's Theorem Exercises p.1113
16.5 Curl and Divergence Exercises p.1121
16.6 Parametric Surfaces and Their Areas Exercises p.1132
16.7 Surface Integrals Exercises p.1144
16.8 Stokes' Theorem Exercises p.1151
16.9 The Divergence Theorem Exercises p.1157
Concept Check p.1160
True-False Quiz p.1160
Review Exercises p.1161
Problems Plus p.1163

Chapter 17

Second-Order Differential Equations

17.1 Second-Order Linear Equations Exercises p.1172
17.2 Nonhomogeneous Linear Equations Exercises p.1179
17.3 Applications of Second-Order Differential Equations Exercises p.1187
17.4 Series Solutions Exercises p.1192
Concept Check p.1193
True-False Quiz p.1193
Review Exercises p.1193
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