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

7th Edition | ISBN: 9780321549280 / 0321549287

4,485

expert-verified solutions in this book

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