Calculus Early Transcendentals: Single Variable – Howard Anton, Irl Bivens, Stephen Davis – 11th Edition

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Calculus: Early Transcendentals, 11th Edition 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.

• 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.

• 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.

• Answer Specific Feedback Questions: Within WileyPLUS with ORION this edition of Anton will feature this new question type allowing students to have customized feedback on the actual work they’re doing.

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Table of Contents

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

APPENDICES
A TRIGONOMETRY SUMMARY
B FUNCTIONS (SUMMARY)
C NEW FUNCTIONS FROM OLD (SUMMARY)
D FAMILIES OF FUNCTIONS (SUMMARY)

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