Calculus: A Complete Course, 7th Edition Calculus: A Complete Course, 7th Edition

Calculus: A Complete Course, 7th Edition

7th Edition | ISBN: 9780321549280 / 0321549287

4,485

expert-verified solutions in this book

Calculus: A Complete Course, 7th Edition
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7th Edition | ISBN: 9780321549280 / 0321549287

4,485

expert-verified solutions in this book

Buy on Amazon.com

Table of Contents

Chapter P

Preliminaries

P-1 Real Numbers and the Real Line Exercises p.10
P-2 Cartesian Coordinates in the Plane Exercises p.16
P-3 Graphs of Quadratic Equations Exercises p.22
P-4 Functions and Their Graphs Exercises p.32
P-5 Combining Functions to Make Functions Exercises p.38
P-6 Polynomials and Rational Functions Exercises p.44
P-7 The Trigonometric Functions Exercises p.56

Chapter 1

Limits And Continuity

1-1 Examples of Velocity, Growth Rate, and Area Exercises p.62
1-2 Limits of Functions Exercises p.70
1-3 Limits at Infinity and Infinite Limits Exercises p.77
1-4 Continuity Exercises p.86
1-5 The Formal Definition of Limit Exercises p.91
Review Exercises p.92
Challenge Problems p.93

Chapter 2

Differentiation

2-1 Tangent Lines and Their Slopes Exercises p.99
2-2 The Derivative Exercises p.106
2-3 Differentiation Rules Exercises p.114
2-4 The Chain Rule Exercises p.119
2-5 Derivatives of Trigonometric Functions Exercises p.124
2-6 Higher-Order Derivatives Exercises p.129
2-7 Using Differentials and Derivatives Exercises p.134
2-8 The Mean-Value Theorem Exercises p.142
2-9 Implicit Differentiation Exercises p.147
2-10 Antiderivatives and Initial-Valued Problems Exercises p.153
2-11 Velocity and Acceleration Exercises p.159
Review Exercises p.160
Challenge Problems p.161

Chapter 3

Transcendental Functions

3-1 Inverse Functions Exercises p.169
3-2 Exponential and Logarithmic Functions Exercises p.173
3-3 The Natural Logarithm and Exponential Exercises p.181
3-4 Growth and Decay Exercises p.188
3-5 The Inverse Trigonometric Functions Exercises p.197
3-6 Hyperbolic Functions Exercises p.202
3-7 Second-Order Linear Des with Constant Coefficients Exercises p.209
Review Exercises p.210
Challenge Problems p.211

Chapter 4

More Applications Of Differentiation

4-1 Related Rates Exercises p.217
4-2 Finding Roots of Equations Exercises p.226
4-3 Indeterminate Forms Exercises p.232
4-4 Extreme Values Exercises p.238
4-5 Concavity and Inflections Exercises p.243
4-6 Sketching the Graphs of a Function Exercises p.251
4-7 Graphing with Computers Exercises p.257
4-8 Extreme-Value Problems Exercises p.263
4-9 Linear Approximations Exercises p.271
4-10 Taylor Polynomials Exercises p.279
4-11 Roundoff Error, Truncation Error, and Computers Exercises p.283
Review Exercises p.284
Challenge Problems p.285

Chapter 5

Integration

5-1 Sums and Sigma Notation Exercises p.292
5-2 Areas as Limits of Sums Exercises p.298
5-3 The Definite Integral Exercises p.304
5-4 Properties of the Definite Integral Exercises p.310
5-5 The Fundamental Theorem of Calculus Exercises p.315
5-6 The Method of Substitution Exercises p.323
5-7 Areas of Plane Regions Exercises p.327
Review Exercises p.328
Challenge Problems p.329

Chapter 6

Techniques Of Integration

6-1 Integration by Parts Exercises p.336
6-2 Integrals of Rational Functions Exercises p.345
6-3 Inverse Substitutions Exercises p.352
6-4 Other Methods for Evaluating Integrals Exercises p.358
6-5 Improper Integrals Exercises p.366
6-6 The Trapezoid and Midpoint Rules Exercises p.374
6-7 Simson's Rule Exercises p.379
6-8 Other Aspects of Approximate Integration Exercises p.385
Review Exercises p.387
Other Review Problems p.388
Challenge Problems p.388

Chapter 7

Applications Of Integration

7-1 Volumes by Slicing-Solids of Revolution Exercises p.398
7-2 More Volumes by Slicing Exercises p.402
7-3 Arc Length and Surface Exercises p.409
7-4 Mass, Moments, and Centre of Mass Exercises p.416
7-5 Centroids Exercises p.421
7-6 Other Physical Applications Exercises p.428
7-7 Applications in Business, Finance, and Ecology Exercises p.432
7-8 Probability Exercises p.444
7-9 First-order Differential Equations Exercises p.452
Review Exercises p.453
Challenge Problems p.454

Chapter 8

Conics, Parametric Curves, And Polar Curves

8-1 Conics Exercises p.467
8-2 Parametric Curves Exercises p.473
8-3 Smooth Parametric Curves and their Slopes Exercises p.478
8-4 Arc lengths and Areas for Parametric Curves Exercises p.482
8-5 Polar Coordinates and Polar Curves Exercises p.488
8-6 Slopes, Areas, and Arc Lengths for Polar Curves Exercises p.492
Review Exercises p.493
Challenge Problems p.493

Chapter 9

Sequences, Series, And Power Series

9-1 Sequences and Convergence Exercises p.502
9-2 Infinite Series Exercises p.509
9-2 Convergence Tests for Positive Series Exercises p.519
9-4 Absolute and Conditional Convergence Exercises p.525
9-5 Power Series Exercises p.536
9-6 Taylor and Maclaurin Series Exercises p.545
9-7 Applications of Taylor and Maclaurin Series Exercises p.549
9-8 The Binomial Theorem and Binomial Series Exercises p.552
9-9 Fourier Series Exercises p.558
Review Exercises p.559
Challenge Problems p.560

Chapter 10

Vectors And Coordinate Geometry In 3-Space

10-1 Analytic Geometry in Three Dimensions Exercises p.567
10-2 Vectors Exercises p.576
10-3 The Cross Product in 3-Space Exercises p.584
10-4 Planes and Lines Exercises p.592
10-5 Quadric Surfaces Exercises p.596
10-6 Cylindrical and Spherical Coordinates Exercises p.600
10-7 A Little Linear Algebra Exercises p.609
10-8 Using Maple for Vector and Matrix Calculations Exercises p.618
Review Exercises p.619
Challenge Problems p.619

Chapter 11

Vector Functions And Curves

11-1 Vector Functions of One Variable Exercises p.627
11-2 Some Applications of Vector Differentiation Exercises p.634
11-3 Curves and Parametrizations Exercises p.641
11-4 Curvature, Torsion, and the Frenet Frame Exercises p.649
11-5 Curvature and Torsion for General Parametrizations Exercises p.655
11-6 Kepler's Laws of Planetary Motion Exercises p.664
Review Exercises p.666
Challenge Problems p.667

Chapter 12

Partial Differentiation

12-1 Functions of Several Variables Exercises p.675
12-2 Limits and Continuity Exercises p.680
12-3 Partial Derivatives Exercises p.687
12-4 Higher-Order Derivatives Exercises p.692
12-5 The Chain Rule Exercises p.702
12-6 Linear Approximations, Differentiability, and Differentials Exercises p.712
12-7 Gradients and Directional Derivatives Exercises p.723
12-8 Implicit Functions Exercises p.734
12-9 Taylor Series and Approximations Exercises p.740
Review Exercises p.740
Challenge Problems p.741

Chapter 13

Applications Of Partial Derivatives

13-1 Extreme Values Exercises p.750
13-2 Extreme Values of Functions Defined on Restricted Domains Exercises p.756
13-3 Lagrange Multipliers Exercises p.764
13-4 The Method of Least Squares Exercises p.770
13-5 Parametric Problems Exercises p.779
13-6 Newton's Method Exercises p.783
13-7 Calculations with Maple Exercises p.788
Review Exercises p.788
Challenge Problems p.789

Chapter 14

Multiple Integration

14-1 Double Integrals Exercises p.795
14-2 Iteration of Double Integrals in Cartesian Coordinates Exercises p.802
14-3 Improper Integrals and a Mean-Value Theorem Exercises p.807
14-4 Double Integrals in Polar Coordinates Exercises p.817
14-5 Triple Integrals Exercises p.823
14-6 Change of variables in Triple Integrals Exercises p.830
14-7 Applications of Multiple Integrals Exercises p.838
Review Exercises p.840
Challenge Problems p.841

Chapter 15

Vector Fields

15-1 Vector and Scalar Fields Exercises p.848
15-2 Conservative Fields Exercises p.857
15-3 Line Integrals Exercises p.861
15-4 Line Integrals of Vector Fields Exercises p.869
15-5 Surfaces and Surface Integrals Exercises p.880
15-6 Oriented Surfaces and Flux Integrals Exercises p.886
Review Exercises p.886
Challenge Problems p.887

Chapter 16

Vector Calculus

16-1 Gradient, Divergence, and Curl Exercises p.896
16-2 Some Identities Involving Grad, Div, and Curl Exercises p.902
16-3 Green's Theorem in the Plane Exercises p.906
16-4 The Divergence Theorem in 3-Space Exercises p.912
16-5 Stoke's Theorem Exercises p.916
16-6 Some Physical Applications of Vector Calculus Exercises p.924
16-7 Orthogonal Curvilinear Coordinates Exercises p.934
Review Exercises p.934
Challenge Problems p.935

Chapter 17

Ordinary Differential Equations

17-1 Classifying Differential Equations Exercises p.940
17-2 Solving First-Order Equations Exercises p.945
17-3 Existence, Uniqueness, and Numerical Methods Exercises p.953
17-4 Differential Equations of Second Order Exercises p.957
17-5 Linear Differential Equations with Constant Coefficients Exercises p.961
17-6 Nonhomogeneous Linear Equations Exercises p.967
17-7 Series Solutions of Differential Equations Exercises p.972
Review Exercises p.972

Chapter Appendix I

Complex Numbers

Exercises p.A-10

Chapter Appendix II

Complex Functions

Exercises p.A-19

Chapter Appendix III

Continuous Functions

Exercises p.A-25

Chapter Appendix IV

The Riemann Integral

Exercises p.A-31
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