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Calculus: A New Horizon

by: Anton, Howard

Calculus: A New Horizon

by: Anton, Howard

ISBN 13:
9780471153061
ISBN 10:
0471153060
Edition: 6th
Format: Hardcover
Copyright: 06/01/1998
Publisher: John Wiley & Sons Inc
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Summary

The new Sixth Edition of Anton2s Calculus is a contemporary text that incorporates the best features of calculus reform, yet preserves the main structure of an established, traditional calculus text. This book is intended for those who want to move slowly into the reform movement. The new edition retains its accessible writing style and a high standard of mathematical precision.

Introduction. Calculus: A New Horizon from Ancient Roots

(15)

Functions

(96)

Functions and the Analysis of Graphical Information

(8)

Properties of Functions

(11)

Graphing Functions on Calculators and Computers; Computer Algebra Systems

(12)

New Functions from Old

(14)

Mathematical Models; Linear Models

(14)

Families of Functions

(18)

Parametric Equations

(13)

Horizon Module: Iteration and Dynamical Systems

106

(5)

Limits and Continuity

111

(58)

Limits (An Intuitive Introduction)

112

(15)

Limits (Computational Techniques)

127

(11)

Limits (Discussed More Rigorously)

138

(10)

Continuity

148

(11)

Limits and Continuity of Trigonometric Functions

159

(10)

The Derivative

169

(56)

Tangent Lines and Rates of Change

170

(7)

The Derivative

177

(12)

Techniques of Differentiation

189

(11)

Derivatives of Trigonometric Functions

200

(4)

The Chain Rule

204

(6)

Local Linear Approximation; Differentials

210

(11)

Horizon Module: Robotics

221

(4)

Logarithmic and Exponential Functions

225

(64)

Inverse Functions

226

(9)

Logarithmic and Exponential Functions

235

(11)

Implicit Differentiation

246

(9)

Derivatives of Logarithmic and Exponential Functions

255

(6)

Derivatives of Inverse Trigonometric Functions

261

(9)

Related Rates

270

(7)

L'Hospital's Rule; Indeterminate Forms

277

(12)

Analysis of Functions and Their Graphs

289

(40)

Analysis of Functions I: Increase, Decrease, and Concavity

290

(9)

Analysis of Functions II: Relative Extrema; First and Second Derivative Tests

299

(7)

Analysis of Functions III: Applying Technology and the Tools of Calculus

306

(23)

Horizon Module: Functions from Data

324

(5)

Applications of the Derivative

329

(48)

Absolute Maxima and Minima

330

(9)

Applied Maximum and Minimum Problems

339

(13)

Rectilinear Motion (Motion Along a Line)

352

(11)

Newton's Method

363

(5)

Rolle's Theorem; Mean-Value Theorem

368

(9)

Integration

377

(84)

An Overview of the Area Problem

378

(4)

The Indefinite Integral; Integral Curves and Direction Fields

382

(9)

Integration by Substitution

391

(6)

Sigma Notation

397

(7)

The Definite Integral

404

(12)

The Fundamental Theorem of Calculus

416

(11)

Rectilinear Motion Revisited; Average Value

427

(14)

Evaluating Definite Integrals by Substitution

441

(5)

Logarithmic Functions from the Integral Point of View

446

(15)

Horizon Module: Blammo the Human Cannonball

457

(4)

Application of the Definite Integral in Geometry, Science, and Engineering

461

(52)

Area Between Two Curves

462

(6)

Volumes by Slicing; Disks and Washers

468

(7)

Volumes by Cylindrical Shells

475

(5)

Length of a Plane Curve

480

(5)

Area of a Surface of Revolution

485

(4)

Work

489

(7)

Fluid Pressure and Force

496

(4)

Hyperbolic Functions and Hanging Cables

500

(13)

Principles of Integral Evaluation

513

(66)

An Overview of Integration Methods

514

(2)

Integration by Parts

516

(6)

Trigonometric Integrals

522

(8)

Trigonometric Substitutions

530

(6)

Integrating Rational Functions by Partial Fractions

536

(7)

Using Tables of Integrals and Computer Algebra Systems

543

Numerical Integration; Simpson's Rule

533

(31)

Improper Integrals

564

(15)

Horizon Module: Railroad Design

576

(3)

Mathematical Modeling with Differential Equations

579

(36)

First-Order Differential Equations and Applications

580

(12)

Direction Fields; Euler's Method

592

(6)

Modeling with Differential Equations

598

(17)

Infinite Series

615

(84)

Sequences

616

(10)

Monotone Sequences

626

(6)

Infinite Series

632

(8)

Convergence Tests

640

(7)

Taylor and Maclaurin Series

647

(9)

The Comparison, Ratio, and Root Tests

656

(6)

Alternating Series; Conditional Convergence

662

(8)

Power Series

670

(6)

Convergence of Taylor Series; Computational Methods

676

(10)

Differentiating and Integrating Power Series; Modeling with Taylor Series

686

(13)

Analytic Geometry in Calculus

699

(60)

Polar Coordinates

700

(13)

Tangent Lines and Arc Length for Parametric and Polar Curves

713

(7)

Area in Polar Coordinates

720

(6)

Conic Sections in Calculus

726

(17)

Conic Sections in Polar Coordinates

743

(16)

Horizon Module: Comet Collision

755

(4)

Three-Dimensional Space; Vectors

759

(70)

Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces

760

(5)

Vectors

765

(11)

Dot Product; Projections

776

(9)

Cross Product

785

(10)

Parametric Equations of Lines

795

(6)

Planes in 3-Space

801

(7)

Quatric Surfaces

808

(11)

Cylindrical and Spherical Coordinates

819

(10)

Vector-Valued Functions

829

(60)

Introduction to Vector-Valued Functions

830

(6)

Calculus of Vector-Valued Functions

836

(7)

Change of Parameter; Arc Length

843

(10)

Unit Tangent, Normal, and Binormal Vectors

853

(5)

Curvature

858

(9)

Motion Along a Curve

867

(13)

Kepler's Laws of Planetary Motion

880

(9)

Partial Derivatives

889

(88)

Functions of Two or More Variables

890

(11)

Limits and Continuity

901

(9)

Partial Derivatives

910

(10)

Differentiability and Chain Rules

920

(10)

Tangent Planes; Total Differentials for Functions of Two Variables

930

(7)

Directional Derivatives and Gradients for Functions of Two Variables

937

(8)

Differentiability, Directional Derivatives, and Gradients for Functions of Three or More Variables

945

(11)

Maxima and Minima of Functions of Two Variables

956

(11)

Lagrange Multipliers

967

(10)

Multiple Integrals

977

(78)

Double Integrals

978

(7)

Double Integrals over Nonrectangular Regions

985

(8)

Double Integrals in Polar Coordinates

993

(7)

Parametric Surface; Surface Area

1000

(12)

Triple Integrals

1012

(7)

Centroid, Center of Gravity, Theorem of Pappus

1019

(10)

Triple Integrals in Cylindrical and Spherical Coordinates

1029

(10)

Change of Variables in Multiple Integrals; Jacobians

1039

(16)

Topics in Vector Calculus

1055

Vector Fields

1056

Line Integrals

1064

Independence of Path; Conservative Vector Fields

1078

Green's Theorem

1088

Surface Integrals

1094

Applications of Surface Integrals; Flux

1101

The Divergence Theorem

1109

Stokes' Theorem

1117

Horizon Module: Hurricane Modeling

1126

Appendix A. Real Numbers, Intervals, and Inequalities

Appendix B. Absolute Value

A11

Appendix C. Coordinate Planes and Lines

A16

Appendix D. Distance, Circles, and Quadratic Equations

A29

Appendix E. Trigonometry Review

A39

Appendix F. Solving Polynomial Equations

A52

Appendix G. Selected Proofs

A57

Answers

A65

Index

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Amazon no longer offers textbook rentals. We do!

Calculus: A New Horizon

Calculus: A New Horizon

9780471153061

0471153060

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Calculus: A New Horizon

Calculus: A New Horizon

9780471153061

0471153060

Summary

Table of Contents

Supplemental Materials

Write a Review

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