# Calculus: Single Variable, 11th Edition

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# Calculus: Single Variable, 11th Edition

ISBN: 978-1-118-88559-8 August 2016 768 Pages

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## Description

Calculus: Late Transcendental, 11th Edition Binder Ready Version strives to increase student comprehension and conceptual understanding through a balance between rigor and clarity of explanations; sound mathematics; and excellent exercises, applications, and examples.  Anton pedagogically approaches Calculus through the Rule of Four, presenting concepts from the verbal, algebraic, visual, and numerical points of view.

Introduction: The Roots of Calculus

1 LIMITS AND CONTINUITY

1.1 Limits (An Intuitive Approach)

1.2 Computing Limits

1.3 Limits at Infinity; End Behavior of a Function

1.4 Limits (Discussed More Rigorously)

1.5 Continuity

1.6 Continuity of Trigonometric Functions

2 THE DERIVATIVE

2.1 Tangent Lines and Rates of Change

2.2 The Derivative Function

2.3 Introduction to Techniques of Differentiation

2.4 The Product and Quotient Rules

2.5 Derivatives of Trigonometric Functions

2.6 The Chain Rule

2.7 Implicit Differentiation

2.8 Related Rates

2.9 Local Linear Approximation; Differentials

3 THE DERIVATIVE IN GRAPHIN AND APPLICATIONS

3.1 Analysis of Function I: Increase, Decrease, and Concavity

3.2 Analysis of Function II: Relative Extrema; Graphing Polynomials

3.3 Analysis of Functions III: Rational Functions, Cups, and Vertical Tangents

3.4 Absolute Maxima and Minima

3.5 Applied Maximum and Minimum Problems

3.6 Rectilinear Motion

3.7 Newton's Method

3.8 Rolle's Theorem; Mean-Value Theorem

4 INTEGRATION

4.1 An Overview of the Area Problem

4.2 The indefinite Integral

4.3 Integration by Substitution

4.4 The Definition of Area as a Limit; Sigma Notation

4.5 The Definite Integral

4.6 The Fundamental Theorem of Calculus

4.7 Rectilinear Motion Revisited Using Integration

4.8 Average Value of a Function and its Applications

4.9 Evaluating Definite Integrals by Substitution

5 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING

5.1 Area Between Two Curves

5.2 Volumes by Slicing; Disks and Washers

5.3 Volumes by Cylindrical Shells

5.4 Length of a Plane Curve

5.5 Area of a Surface of Revolution

5.6 Work

5.7 Moments, Centers of Gravity, and Centroids

5.8 Fluid Pressure and Force

6 EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS

6.1 Exponential and Logarithmic Functions

6.2 Derivatives and Integrals Involving Logarithmic Functions

6.3 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions

6.4 Graphs and Applications Involvig Logarithmic and Exponential Functions

6.5 LHopital's Rule; Indeterminate Forms

6.6 Logarithmic and Other Functions Defined by Integrals

6.7 Derivatives and Integrals Involving Inverse Trigonometric Functions

6.8 Hyperbolic Functions and Hanging Cables

7 PRINCIPLES OF INTEGRAL EVALUATION

7.1 An Overview of Integration Methods

7.2 Integration by Parts

7.3 Integrating Trigonometric Functions

7.4 Trigonometric Substitutions

7.5 Integrating Rational Functions by Partial Fractions

7.6 Using Computer Algebra Systems and Tables of Integrals

7.7 Numerical Integration; Simpson’s Rule

7.8 Improper Integrals

8 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS

8.1 Modeling with Differential Equations

8.2 Separation of Variables

8.3 Slope Fields; Euler’s Method

8.4 First-Order Differential Equations and Applications

9 INFINITE SERIES

9.1 Sequences

9.2 Monotone Sequences

9.3 Infinite Series

9.4 Convergence Tests

9.5 The Comparison, Ratio, and Root Tests

9.6 Alternating Series; Absolute and Conditional Convergence

9.7 Maclaurin and Taylor Polynomials

9.8 Maclaurin and Taylor Series; Power Series

9.9 Convergence of Taylor Series

9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series

10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS

10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves

10.2 Polar Coordinates

10.3 Tangent Lines, Arc Length, and Area for Polar Curves

10.4 Conic Sections

10.5 Rotation of Axes; Second-Degree Equations

10.6 Conic Sections in Polar Coordinates

11 THREE-DIMENSIONAL SPACE; VECTORS

11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces

11.2 Vectors

11.3 Dot Product; Projections

11.4 Cross Product

11.5 Parametric Equations of Lines

11.6 Planes in 3-Space

11.8 Cylindrical and Spherical Coordinates

12 VECTOR-VALUED FUNCTIONS

12.1 Introduction to Vector-Valued Functions

12.2 Calculus of Vector-Valued Functions

12.3 Change of Parameter; Arc Length

12.4 Unit Tangent, Normal, and Binormal Vectors

12.5 Curvature

12.6 Motion Along a Curve

12.7 Kepler’s Laws of Planetary Motion

13 PARTIAL DERIVATIVES

13.1 Functions of Two or More Variables

13.2 Limits and Continuity

13.3 Partial Derivatives

13.4 Differentiability, Differentials, and Local Linearity

13.5 The Chain Rule

13.6 Directional Derivatives and Gradients

13.7 Tangent Planes and Normal Vectors

13.8 Maxima and Minima of Functions of Two Variables

13.9 Lagrange Multipliers

14 MULTIPLE INTEGRALS

14.1 Double Integrals

14.2 Double Integrals over Nonrectangular Regions

14.3 Double Integrals in Polar Coordinates

14.4 Surface Area; Parametric Surfaces

14.5 Triple Integrals

14.6 Triple Integrals in Cylindrical and Spherical Coordinates

14.7 Change of Variables in Multiple Integrals; Jacobians

14.8 Centers of Gravity Using Multiple Integrals

15 TOPICS IN VECTOR CALCULUS

15.1 Vector Fields

15.2 Line Integrals

15.3 Independence of Path; Conservative Vector Fields

15.4 Green’s Theorem

15.5 Surface Integrals

15.6 Applications of Surface Integrals; Flux

15.7 The Divergence Theorem

15.8 Stokes’ Theorem

APPENDICES

A TRIGONOMETRY SUMMARY

B FUNCTIONS (SUMMARY)

C NEW FUNCTIONS FROM OLD (SUMMARY)

D FAMILIES OF FUNCTIONS (SUMMARY)

ANSWERS TO ODD-NUMBERED EXERCISES

INDEX

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Video Program: Videos of worked examples and problems covering the subject material in the Single Variable chapters of the 11th edition.

Math Enhancements: Measure conceptual understanding in an online learning environment, through intelligent tutoring, graphing enhancements, improvements to Show Work Whiteboard, expanded test bank functionality, and enhanced grading rules functionality.

Pre-created activities encourage learning outside of the classroom through gradable reading assignment questions and more than 3,000 end-of-chapter problems coded algorithmically.

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Relevant student study tools and learning resources: Ensures positive learning outcomes including: graphing and math Palette tutorial videos; interactive illustrations; calculus applets; and student practice activities.

Technology Exercises: In the textbook, these exercises—marked with an icon for easy identification—are designed to be solved using either a graphing calculator or a computer algebra system such as Mathematics, Maple, or Derive.