Calculus Early Transcendentals Single Variable, 9th Edition

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  • Edition: 9th
  • Format: Hardcover
  • Copyright: 2008-11-01
  • Publisher: Wiley
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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
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 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'H˘pital'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
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
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
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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