#### Calculus: Early Transcendentals, 11th Edition

*By Howard Anton, Irl C. Bivens, Stephen Davis
*

Researchers and educators agree that it takes more than academic knowledge to be prepared for college—intrapersonal competencies like conscientiousness have been proven to be strong determinants of success. WileyPLUS with ORION for **Calculus**helps you identify students’ proficiency early in the semester and intervene as needed.

Want to learn more about WileyPLUS? Click Here

New video program helps student see what they learn

Videos of worked examples and problems highlight specific learning objectives in the Single Variable chapters of the Eleventh Edition.

Students get the practice they need to master concepts

ORION Algebra and Trigonometry Refresher Module helps students master algebra, trigonometry, and polynomial equations. With ORION, students can create a personalized study plan and instructors can use class time to focus on Calculus.

Students get feedback at the point of learning

New Answer-Specific Feedback Questions give students customized feedback on the actual work they’re doing at the point of learning.

#### What’s New

• ** WileyPLUS **is a research-based online environment for effective teaching and learning. Interactive study tools and resources–including the complete online textbook–give students more value for their money.

• **Industry-leading support from WileyPLUS with ORION: **Resources and personal support are available from the first day of class onward through technical support;

*WileyPLUS*account managers;

*WileyPLUS*with QuickStart; and

*WileyPLUS*Student Partner Program.

• **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.

• **Quick Check Exercises: **Each exercise set begins with approximately five exercises (answers included) that are designed to provide student with an immediate assessment of whether they have mastered key ideas form the section.

• **Career Preparation:** This program has been created at a mathematical level that will prepare students for a wide variety of careers that require a sound mathematical background, including engineering, the various sciences, and business.

**Howard Anton** obtained his B.A. from Lehigh University, his M.A. from the University of Illinois, and his Ph.D. from the Polytechnic Institute of Brooklyn, all in mathematics. He worked in the manned space program at Cape Canaveral in the early 1960’s. In 1968 he became a research professor of mathematics at Drexel University in Philadelphia, where he taught and did mathematical research for 15 years. In 1983 he left Drexel as a Professor Emeritus of Mathematics to become a full-time writer of mathematical textbooks. There are now more than 150 versions of his books in print, including translations into Spanish, Arabic, Portuguese, French, German, Chinese, Japanese, Hebrew, Italian, and Indonesian. He was awarded a Textbook Excellence Award in 1994 by the Textbook Authors Association, and in 2011 that organization awarded his Elementary Linear Algebra text its McGuffey Award.

**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

1.7 Inverse Trigonometric Functions

1.8 Exponential and Logarithmic 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

**3 TOPICS IN DIFFERENTIATION**

3.1 Implicit Differentiation

3.2 Derivatives of Logarithmic Functions

3.3 Derivatives of Exponential and Inverse Trigonometric Functions

3.4 Related Rates

3.5 Local Linear Approximation; Differentials

3.6 L’Hôpital’s Rule; Indeterminate Forms

**4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS**

4.1 Analysis of Functions I: Increase, Decrease, and Concavity

4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials

4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents

4.4 Absolute Maxima and Minima

4.5 Applied Maximum and Minimum Problems

4.6 Rectilinear Motion

4.7 Newton’s Method

4.8 Rolle’s Theorem; Mean-Value Theorem

**5 INTEGRATION**

5.1 An Overview of the Area Problem

5.2 The Indefinite Integral

5.3 Integration by Substitution

5.4 The Definition of Area as a Limit; Sigma Notation

5.5 The Definite Integral

5.6 The Fundamental Theorem of Calculus

5.7 Rectilinear Motion Revisited Using Integration

5.8 Average Value of a Function and its Applications

5.9 Evaluating Definite Integrals by Substitution

5.10 Logarithmic and Other Functions Defined by Integrals

**6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING**

6.1 Area Between Two Curves

6.2 Volumes by Slicing; Disks and Washers

6.3 Volumes by Cylindrical Shells

6.4 Length of a Plane Curve

6.5 Area of a Surface of Revolution

6.6 Work

6.7 Moments, Centers of Gravity, and Centroids

6.8 Fluid Pressure and Force

6.9 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

11.7 Quadric Surfaces

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)