| |
| |
| |
Before Calculus | |
| |
| |
| |
Functions | |
| |
| |
| |
New Functions from Old | |
| |
| |
| |
Families of Functions | |
| |
| |
| |
Inverse Functions | |
| |
| |
| |
Limits And Continuity | |
| |
| |
| |
Limits (An Intuitive Approach) | |
| |
| |
| |
Computing Limits | |
| |
| |
| |
Limits at Infinity; End Behavior of a Function | |
| |
| |
| |
Limits (Discussed More Rigorously) | |
| |
| |
| |
Continuity | |
| |
| |
| |
Continuity of Trigonometric Functions | |
| |
| |
| |
The Derivative | |
| |
| |
| |
Tangent Lines and Rates of Change | |
| |
| |
| |
The Derivative Function | |
| |
| |
| |
Introduction to Techniques of Differentiation | |
| |
| |
| |
The Product and Quotient Rules | |
| |
| |
| |
Derivatives of Trigonometric Functions | |
| |
| |
| |
The Chain Rule | |
| |
| |
| |
Implicit Differentiation | |
| |
| |
| |
Related Rates | |
| |
| |
| |
Local Linear Approximation; Differentials | |
| |
| |
| |
The Derivative In Graphing And Applications | |
| |
| |
| |
Analysis of Functions I: Increase, Decrease, and Concavity | |
| |
| |
| |
Analysis of Functions II: Relative Extrema; Graphing Polynomials | |
| |
| |
| |
Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents | |
| |
| |
| |
Absolute Maxima and Minima | |
| |
| |
| |
Applied Maximum and Minimum Problems | |
| |
| |
| |
Rectilinear Motion | |
| |
| |
| |
Newton's Method | |
| |
| |
| |
Rolle's Theorem; Mean-Value Theorem | |
| |
| |
| |
Integration | |
| |
| |
| |
An Overview of the Area Problem | |
| |
| |
| |
The Indefinite Integral | |
| |
| |
| |
Integration by Substitution | |
| |
| |
| |
The Definition of Area as a Limit; Sigma Notation | |
| |
| |
| |
The Definite Integral | |
| |
| |
| |
The Fundamental Theorem of Calculus | |
| |
| |
| |
Rectilinear Motion Revisited Using Integration | |
| |
| |
| |
Average Value of a Function and its Applications | |
| |
| |
| |
Evaluating Definite Integrals by Substitution | |
| |
| |
| |
Applications Of The Definite Integral In Geometry, Science, And Engineering | |
| |
| |
| |
Area Between Two Curves | |
| |
| |
| |
Volumes by Slicing; Disks and Washers | |
| |
| |
| |
Volumes by Cylindrical Shells | |
| |
| |
| |
Length of a Plane Curve | |
| |
| |
| |
Area of a Surface of Revolution | |
| |
| |
| |
Work | |
| |
| |
| |
Moments, Centers of Gravity, and Centroids | |
| |
| |
| |
Fluid Pressure and Force | |
| |
| |
| |
Exponential, Logarithmic, And Inverse Trigonometric Functions | |
| |
| |
| |
Exponential and Logarithmic Functions | |
| |
| |
| |
Derivatives and Integrals Involving Logarithmic Functions | |
| |
| |
| |
Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions | |
| |
| |
| |
Graphs and Applications Involving Logarithmic and Exponential Functions | |
| |
| |
| |
L'H�pital's Rule; Indeterminate Forms | |
| |
| |
| |
Logarithmic and Other Functions Defined by Integrals | |
| |
| |
| |
Derivatives and Integrals Involving Inverse Trigonometric Functions | |
| |
| |
| |
Hyperbolic Functions and Hanging Cables | |
| |
| |
| |
Principles Of Integral Evaluation | |
| |
| |
| |
An Overview of Integration Methods | |
| |
| |
| |
Integration by Parts | |
| |
| |
| |
Integrating Trigonometric Functions | |
| |
| |
| |
Trigonometric Substitutions | |
| |
| |
| |
Integrating Rational Functions by Partial Fractions | |
| |
| |
| |
Using Computer Algebra Systems and Tables of Integrals | |
| |
| |
| |
Numerical Integration; Simpson's Rule | |
| |
| |
| |
Improper Integrals | |
| |
| |
| |
Mathematical Modeling With Differential Equations | |
| |
| |
| |
Modeling with Differential Equations | |
| |
| |
| |
Separation of Variables | |
| |
| |
| |
Slope Fields; Euler's Method | |
| |
| |
| |
First-Order Differential Equations and Applications | |
| |
| |
| |
Infinite Series | |
| |
| |
| |
Sequences | |
| |
| |
| |
Monotone Sequences | |
| |
| |
| |
Infinite Series | |
| |
| |
| |
Convergence Tests | |
| |
| |
| |
The Comparison, Ratio, and Root Tests | |
| |
| |
| |
Alternating Series; Absolute and Conditional Convergence | |
| |
| |
| |
Maclaurin and Taylor Polynomials | |
| |
| |
| |
Maclaurin and Taylor Series; Power Series | |
| |
| |
| |
Convergence of Taylor Series | |
| |
| |
| |
Differentiating and Integrating Power Series; Modeling with Taylor Series | |
| |
| |
| |
Parametric And Polar Curves; Conic Sections | |
| |
| |
| |
Parametric Equations; Tangent Lines and Arc Length for Parametric Curves | |
| |
| |
| |
Polar Coordinates | |
| |
| |
| |
Tangent Lines, Arc Length, and Area for Polar Curves | |
| |
| |
| |
Conic Sections | |
| |
| |
| |
Rotation of Axes; Second-Degree Equations | |
| |
| |
| |
Conic Sections in Polar Coordinates 754 A APPENDICES A GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRA SYSTEMS A1 B TRIGONOMETRY REVIEW A13 C SOLVING POLYNOMIAL EQUATIONS A27 D SELECTED PROOFS A34 ANSWERS TO ODD-NUMBERED EXERCISES A45 | |
| |
| |
Index | |
| |
| |
Web Appendices (online only) | |
| |
| |
Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS | |
| |
| |
| |
Real Numbers, Intervals, And Inequalities | |
| |
| |
| |
Absolute Value | |
| |
| |
| |
Coordinate Planes, Lines, And Linear Functions | |
| |
| |
| |
Distance, Circles, And Quadratic Equations | |
| |
| |
| |
Early Parametric Equations Option | |
| |
| |
| |
Mathematical Models | |
| |
| |
| |
The Discriminant | |
| |
| |
| |
Second-Order Linear Homogeneous Differential Equations | |
| |
| |
Web Projects: Expanding the Calculus Horizon (online only) | |
| |
| |
Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS | |
| |
| |
Blammo The Human Cannonball | |
| |
| |
Comet Collision | |
| |
| |
Hurricane Modeling | |
| |
| |
Iteration And Dynamical Systems | |
| |
| |
Railroad Design | |
| |
| |
Robotics | |