Calculus Early Transcendentals Single Variable, 9th Edition

by Howard Anton (Drexel University); Irl C. Bivens; Stephen Davis (Davidson College)

• ISBN13: 9780470182048
• ISBN10: 0470182040
• Edition: 9th
• Format: Hardcover
• Copyright: 2008-11-01
• Publisher: Wiley

Summary

The ninth edition continues to provide engineers with an accessible resource for learning calculus. The book includes carefully worked examples and special problem types that help improve comprehension. New applied exercises demonstrate the usefulness of the mathematics. Additional summary tables with step-by-step details are also incorporated into the chapters to make the concepts easier to understand. The Quick Check and Focus on Concepts exercises have been updated as well. Engineers become engaged in the material because of the easy-to-read style and real-world examples.

Table of Contents

Before Calculus

Functions

New Functions from Old

Families of Functions

Inverse Functions; Inverse Trigonometric Functions

Exponential and Logarithmic 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, Exponential, and Inverse 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

Topics in Differentiation

Implicit Differentiation

Derivatives of Logarithmic Functions

Derivatives of Exponential and Inverse Trigonometric Functions

Related Rates

Local Linear Approximation; Differentials

L'Hôpital's Rule; Indeterminate Forms

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

Logarithmic and Other Functions Defined by Integrals

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

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

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