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What is included with this book?
Preface | p. ix |
Preliminaries | p. 1 |
Real Numbers, Estimation, and Logic | p. 1 |
Inequalities and Absolute Values | p. 8 |
The Rectangular Coordinate System | p. 16 |
Graphs of Equations | p. 24 |
Functions and Their Graphs | p. 29 |
Operations on Functions | p. 35 |
Trigonometric Functions | p. 41 |
Chapter Review | p. 51 |
Review and Preview Problems | p. 54 |
Limits | p. 55 |
Introduction to Limits | p. 55 |
Rigorous Study of Limits | p. 61 |
Limit Theorems | p. 68 |
Limits Involving Trigonometric Functions | p. 73 |
Limits at Infinity; Infinite Limits | p. 77 |
Continuity of Functions | p. 82 |
Chapter Review | p. 90 |
Review and Preview Problems | p. 92 |
The Derivative | p. 93 |
Two Problems with One Theme | p. 93 |
The Derivative | p. 100 |
Rules for Finding Derivatives | p. 107 |
Derivatives of Trigonometric Functions | p. 114 |
The Chain Rule | p. 118 |
Higher-Order Derivatives | p. 125 |
Implicit Differentiation | p. 130 |
Related Rates | p. 135 |
Differentials and Approximations | p. 142 |
Chapter Review | p. 147 |
Review and Preview Problems | p. 150 |
Applications of the Derivative | p. 151 |
Maxima and Minima | p. 151 |
Monotonicity and Concavity | p. 155 |
Local Extrema and Extrema on Open Intervals | p. 162 |
Practical Problems | p. 167 |
Graphing Functions Using Calculus | p. 178 |
The Mean Value Theorem for Derivatives | p. 185 |
Solving Equations Numerically | p. 190 |
Antiderivatives | p. 197 |
Introduction to Differential Equations | p. 203 |
Chapter Review | p. 209 |
Review and Preview Problems | p. 214 |
The Definite Integral | p. 215 |
Introduction to Area | p. 215 |
The Definite Integral | p. 224 |
The First Fundamental Theorem of Calculus | p. 232 |
The Second Fundamental Theorem of Calculus and the Method of Substitution | p. 243 |
The Mean Value Theorem for Integrals and the Use of Symmetry | p. 253 |
Numerical Integration | p. 260 |
Chapter Review | p. 270 |
Review and Preview Problems | p. 274 |
Applications of the Integral | p. 275 |
The Area of a Plane Region | p. 275 |
Volumes of Solids: Slabs, Disks, Washers | p. 281 |
Volumes of Solids of Revolution: Shells | p. 288 |
Length of a Plane Curve | p. 294 |
Work and Fluid Force | p. 301 |
Moments and Center of Mass | p. 308 |
Probability and Random Variables | p. 316 |
Chapter Review | p. 322 |
Review and Preview Problems | p. 324 |
Transcendental Functions | p. 325 |
The Natural Logarithm Function | p. 325 |
Inverse Functions and Their Derivatives | p. 331 |
The Natural Exponential Function | p. 337 |
General Exponential and Logarithmic Functions | p. 342 |
Exponential Growth and Decay | p. 347 |
First-Order Linear Differential Equations | p. 355 |
Approximations for Differential Equations | p. 359 |
The Inverse Trigonometric Functions and Their Derivatives | p. 365 |
The Hyperbolic Functions and Their Inverses | p. 374 |
Chapter Review | p. 380 |
Review and Preview Problems | p. 382 |
Techniques of Integration | p. 383 |
Basic Integration Rules | p. 383 |
Integration by Parts | p. 387 |
Some Trigonometric Integrals | p. 393 |
Rationalizing Substitutions | p. 399 |
Integration of Rational Functions Using Partial Fractions | p. 404 |
Strategies for Integration | p. 411 |
Chapter Review | p. 419 |
Review and Preview Problems | p. 422 |
Indeterminate Forms and Improper Integrals | p. 423 |
Indeterminate Forms of Type 0/0 | p. 423 |
Other Indeterminate Forms | p. 428 |
Improper Integrals: Infinite Limits of Integration | p. 433 |
Improper Integrals: Infinite Integrands | p. 442 |
Chapter Review | p. 446 |
Review and Preview Problems | p. 448 |
Infinite Series | p. 449 |
Infinite Sequences | p. 449 |
Infinite Series | p. 455 |
Positive Series: The Integral Test | p. 463 |
Positive Series: Other Tests | p. 468 |
Alternating Series, Absolute Convergence, and Conditional Convergence | p. 474 |
Power Series | p. 479 |
Operations on Power Series | p. 484 |
Taylor and Maclaurin Series | p. 489 |
The Taylor Approximation to a Function | p. 497 |
Chapter Review | p. 504 |
Review and Preview Problems | p. 508 |
Conics and Polar Coordinates | p. 509 |
The Parabola | p. 509 |
Ellipses and Hyperbolas | p. 513 |
Translation and Rotation of Axes | p. 523 |
Parametric Representation of Curves in the Plane | p. 530 |
The Polar Coordinate System | p. 537 |
Graphs of Polar Equations | p. 542 |
Calculus in Polar Coordinates | p. 547 |
Chapter Review | p. 552 |
Review and Preview Problems | p. 554 |
Geometry in Space and Vectors | p. 555 |
Cartesian Coordinates in Three-Space | p. 555 |
Vectors | p. 560 |
The Dot Product | p. 566 |
The Cross Product | p. 574 |
Vector-Valued Functions and Curvilinear Motion | p. 579 |
Lines and Tangent Lines in Three-Space | p. 589 |
Curvature and Components of Acceleration | p. 593 |
Surfaces in Three-Space | p. 603 |
Cylindrical and Spherical Coordinates | p. 609 |
Chapter Review | p. 613 |
Review and Preview Problems | p. 616 |
Derivatives for Functions of Two or More Variables | p. 617 |
Functions of Two or More Variables | p. 617 |
Partial Derivatives | p. 624 |
Limits and Continuity | p. 629 |
Differentiability | p. 635 |
Directional Derivatives and Gradients | p. 641 |
The Chain Rule | p. 647 |
Tangent Planes and Approximations | p. 652 |
Maxima and Minima | p. 657 |
The Method of Lagrange Multipliers | p. 666 |
Chapter Review | p. 672 |
Review and Preview Problems | p. 674 |
Multiple Integrals | p. 675 |
Double Integrals over Rectangles | p. 675 |
Iterated Integrals | p. 680 |
Double Integrals over Nonrectangular Regions | p. 684 |
Double Integrals in Polar Coordinates | p. 691 |
Applications of Double Integrals | p. 696 |
Surface Area | p. 700 |
Triple Integrals in Cartesian Coordinates | p. 706 |
Triple Integrals in Cylindrical and Spherical Coordinates | p. 713 |
Change of Variables in Multiple Integrals | p. 718 |
Chapter Review | p. 728 |
Review and Preview Problems | p. 730 |
Vector Calculus | p. 731 |
Vector Fields | p. 731 |
Line Integrals | p. 735 |
Independence of Path | p. 742 |
Green's Theorem in the Plane | p. 749 |
Surface Integrals | p. 755 |
Gauss's Divergence Theorem | p. 764 |
Stokes's Theorem | p. 770 |
Chapter Review | p. 773 |
Differential Equations | p. 775 |
Linear Homogeneous Equations | p. 775 |
Nonhomogeneous Equations | p. 779 |
Applications of Second-Order Equations | p. 783 |
Chapter Review | p. 788 |
Appendix | p. A-1 |
Mathematical Induction | p. A-1 |
Proofs of Several Theorems | p. A-3 |
Answers to Odd-Numbered Problems | p. A-7 |
Index | p. I-1 |
Photo Credits | P-1 |
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