Calculus: Early Transcendental Single Variable / Edition 11

by Howard Anton, Irl C. Bivens, Stephen Davis

Overview

Calculus: Early Transcendentals, Binder Ready Version, 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. This text is an unbound, three hole punched version. Access to WileyPLUS sold separately.

Product Details

ISBN-13:	9781118885277
Publisher:	Wiley
Publication date:	02/29/2016
Edition description:	11th ed.
Pages:	784
Product dimensions:	8.40(w) x 10.90(h) x 0.60(d)

About the Author

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.

Table of Contents

1 Limits and Continuity 1

1.1 Limits (An Intuitive Approach) 1

1.2 Computing Limits 13

1.3 Limits at Infinity; End Behavior of a Function 22

1.4 Limits (Discussed More Rigorously) 31

1.5 Continuity 40

1.6 Continuity of Trigonometric Functions 51

1.7 Inverse Trigonometric Functions 56

1.8 Exponential and Logarithmic Functions 63

2 The Derivative 79

2.1 Tangent Lines and Rates of Change 79

2.2 The Derivative Function 89

2.3 Introduction to Techniques of Differentiation 100

2.4 The Product and Quotient Rules 108

2.5 Derivatives of Trigonometric Functions 113

2.6 The Chain Rule 118

3 Topics In Differentiation 129

3.1 Implicit Differentiation 129

3.2 Derivatives of Logarithmic Functions 135

3.3 Derivatives of Exponential and Inverse Trigonometric Functions 140

3.4 Related Rates 146

3.5 Local Linear Approximation; Differentials 153

3.6 L’Hôpital’s Rule; Indeterminate Forms 160

4 The Derivative In Graphing and Applications 172

4.1 Analysis of Functions I: Increase, Decrease, and Concavity 172

4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 183

4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 192

4.4 Absolute Maxima and Minima 204

4.5 Applied Maximum and Minimum Problems 212

4.6 Rectilinear Motion 225

4.7 Newton’s Method 233

4.8 Rolle’s Theorem; Mean-Value Theorem 239

5 Integration 253

5.1 An Overview of the Area Problem 253

5.2 The Indefinite Integral 258

5.3 Integration by Substitution 268

5.4 The Definition of Area as a Limit; Sigma Notation 275

5.5 The Definite Integral 285

5.6 The Fundamental Theorem of Calculus 294

5.7 Rectilinear Motion Revisited Using Integration 306

5.8 Average Value of a Function and its Applications 314

5.9 Evaluating Definite Integrals by Substitution 319

5.10 Logarithmic and Other Functions Defined by Integrals 325

6 Applications of the Definite Integral In Geometry, Science, and Engineering 341

6.1 Area Between Two Curves 341

6.2 Volumes by Slicing; Disks and Washers 349

6.3 Volumes by Cylindrical Shells 358

6.4 Length of a Plane Curve 364

6.5 Area of a Surface of Revolution 370

6.6 Work 375

6.7 Moments, Centers of Gravity, and Centroids 383

6.8 Fluid Pressure and Force 392

6.9 Hyperbolic Functions and Hanging Cables 398

7 Principles of Integral Evaluation 412

7.1 An Overview of Integration Methods 412

7.2 Integration by Parts 415

7.3 Integrating Trigonometric Functions 423

7.4 Trigonometric Substitutions 431

7.5 Integrating Rational Functions by Partial Fractions 437

7.6 Using Computer Algebra Systems and Tables of Integrals 445

7.7 Numerical Integration; Simpson’s Rule 454

7.8 Improper Integrals 467

8 Mathematical Modeling With Differential Equations 481

8.1 Modeling with Differential Equations 481

8.2 Separation of Variables 487

8.3 Slope Fields; Euler’s Method 498

8.4 First-Order Differential Equations and Applications 504

9 Infinite Series 514

9.1 Sequences 514

9.2 Monotone Sequences 524

9.3 Infinite Series 531

9.4 Convergence Tests 539

9.5 The Comparison, Ratio, and Root Tests 547

9.6 Alternating Series; Absolute and Conditional Convergence 553

9.7 Maclaurin and Taylor Polynomials 563

9.8 Maclaurin and Taylor Series; Power Series 573

9.9 Convergence of Taylor Series 582

9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 591

10 Parametric and Polar Curves; Conic Sections 605

10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 605

10.2 Polar Coordinates 617

10.3 Tangent Lines, Arc Length, and Area for Polar Curves 630

10.4 Conic Sections 639

10.5 Rotation of Axes; Second-Degree Equations 656

10.6 Conic Sections in Polar Coordinates 661

A Appendices

A Trigonometry Review (Summary) A1

B Functions (Summary) A8

C New Functions From Old (Summary) A11

D Families of Functions (Summary) A16

E Inverse Functions (Summary) A23

Answers To Odd-Numbered Exercises A28

Index I-1

Web Appendices (online only)
Available for download at www.wiley.com/college/anton or at www.howardanton.com and in WileyPLUS.

A Trigonometry Review

B Functions

C New Functions From Old

D Families of Functions

E Inverse Functions

F Real Numbers, Intervals, and Inequalities

G Absolute Value

H Coordinate Planes, Lines, and Linear Functions

I Distance, Circles, and Quadratic Equations

J Solving Polynomial Equations

K Graphing Functions Using Calculators and Computer Algebra Systems

L Selected Proofs

M Early Parametric Equations Option

N Mathematical Models

O The Discriminant

P Second-Order Linear Homogeneous Differential Equations

Chapter Web Projects: Expanding the Calculus Horizon (online only)
Available for download at www.wiley.com/college/anton or at www.howardanton.com and in WileyPLUS.

Robotics – Chapter 2

Railroad Design – Chapter 7

Iteration and Dynamical Systems – Chapter 9

Comet Collision – Chapter 10

Blammo the Human Cannonball – Chapter 12

Hurricane Modeling – Chapter 15