Calculus

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780201549775 | 0201549778
Cover: Hardcover
Copyright: 1/1/1994

Rent

(Recommended)

$55.89

Term

Due

Price

Semester

Aug 2

$55.89

Quarter

Jul 19

$53.10

Short Term

Jun 21

$50.29

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.
Buy Used

In Stock Usually Ships in 24 Hours.

$37.25

Written by two of today's most experienced and respected calculus educators, every chapter of this new edition emphasizes the book's realistic approach to calculus. Real applications and exercises, a realistic problem-solving framework, and real-world chapter openers make Calculus, Second Edition the choice for today's students.

Prerequisites for Calculus

Overview

(1)

Coordinates, Increments, and Lines

(10)

Functions and Graphs

(11)

Trigonometric Functions

(8)

Shifts, Circles, and Parabolas

(11)

Calculus and Computation

(7)

Absolute Values (Magnitudes) and Target Values

(15)

For Your Review

(1)

Practice Exercises

(5)

Limits and Continuity

Overview

(1)

Limits of Function Values

(13)

Limits Involving Infinity

(8)

The Sandwich Theorem and (sinθ)/θ

(6)

Continuous Functions

(11)

Defining Limits Formally with Epsilons and Deltas

101

(12)

For Your Review

109

(1)

Practice Exercises

109

(4)

Derivatives

Overview

113

(1)

Slopes, Tangent Lines, and Derivatives

113

(13)

Differentiation Rules

126

(12)

Velocity, Speed, and Other Rates of Change

138

(14)

Derivatives of Trigonometric Functions

152

(7)

The Chain Rule

159

(9)

Implicit Differentiation and Fractional Powers

168

(8)

Linearizations and Differentials

176

(11)

Newton's Method

187

(14)

For Your Review

195

(1)

Practice Exercises

195

(6)

Applications of Derivatives

Overview

201

(1)

Related Rates of Change

201

(8)

Extreme Values of Functions

209

(9)

How Y' and Y'' Determine the Shape of a Graph

218

(9)

Graphs of Rational Functions--Asymptotes and Dominant Terms

227

(7)

Optimization

234

(12)

The Mean Value Theorem

246

(7)

Antiderivatives, Differential Equations, and Modeling

253

(18)

For Your Review

265

(1)

Practice Exercises

266

(5)

Integration

Overview

271

(1)

Estimating with Finite Sums

271

(11)

Riemann Sums and Definite Integrals

282

(12)

Basic Properties, Area, and the Mean Value Theorem for Integrals

294

(8)

The Fundamental Theorem of Calculus

302

(11)

Indefinite Integrals

313

(9)

Integration by Substitution--Running the Chain Rule Backward

322

(9)

Numerical Integration

331

(16)

For Your Review

342

(1)

Practice Exercises

342

(5)

Transcendental Functions

Overview

347

(1)

Exponential Functions and the Derivative of ex

347

(8)

Inverse Functions and Their Derivatives

355

(6)

Logarithmic Functions and the Derivative of ln x

361

(12)

Exponential and Logarithmic Integrals; ln

373

(6)

Growth and Decay

379

(9)

L'Hopital's Rule

388

(7)

Relative Rates of Growth

395

(6)

Inverse Trigonometric Functions

401

(8)

Derivatives of Inverse Trigonometric Functions; Integrals

409

(7)

Hyperbolic Functions

416

(8)

First Order Differential Equations

424

(15)

For your Review

434

(1)

Practice Exercises

435

(4)

Applications of Integration

Overview

439

(1)

Areas Between Curves

439

(7)

Volumes of Solids of Revolution --- Disks and Washers

446

(10)

Cylindrical Shells --- An Alternative to Washers

456

(6)

Curve Length and Surface Area

462

(10)

Work

472

(7)

Fluid Pressures and Fluid Forces

479

(7)

Centers of Mass

486

(11)

The Basic Pattern and Other Modeling Applications

497

(14)

For Your Review

507

(1)

Practice Exercises

507

(4)

Techniques of Integration

Overview

511

(1)

Basic Integration Formulas

511

(6)

Integration by Parts

517

(7)

Partial Fractions

524

(5)

Trigonometric Substitutions

529

(5)

Integral Tables

534

(8)

Improper Integrals

542

(15)

For Your Review

552

(1)

Practice Exercises

552

(5)

Infinite Series

Overview

557

(1)

Sequences

557

(10)

Infinite Series

567

(9)

Series with Nonnegative Terms---Comparison and Integral Tests

576

(9)

Series with Nonnegative Terms---Ratio and Root Tests

585

(6)

Alternating Series and Absolute Convergence

591

(6)

Power Series

597

(8)

Taylor and Maclaurin Series

605

(14)

Calculations with Taylor Series

619

(10)

For Your Review

626

(1)

Practice Exercises

626

(3)

Conic Sections, Parametrized Curves, and Polar Coordinates

Overview

629

(1)

Conic Sections and Quadratic Equations

629

(16)

The Graphs of Quadratic Equations in x and y; Rotations About the Origin

645

(5)

Parametrizations of Curves

650

(6)

Calculus with Parametrized Curves

656

(6)

Polar Coordinates

662

(5)

Polar Graphs

667

(7)

Polar Equations for Conic Sections

674

(6)

Integration in Polar Coordinates

680

(11)

For Your Review

686

(1)

Practice Exercises

687

(4)

Vectors and Analytic Geometry in Space

Overview

691

(1)

Vectors in the Plane

691

(9)

Cartesian (Rectangular) Coordinates and Vectors in Space

700

(10)

Dot Products

710

(8)

Cross Products

718

(6)

Lines and Planes in Space

724

(7)

Surfaces in Space

731

(10)

Cylindrical and Spherical Coordinates

741

(10)

For Your Review

746

(1)

Practice Exercises

747

(4)

Vector-Valued Functions

Overview

751

(1)

Vector-Valued Functions and Space Curves

751

(11)

Modeling Projectile Motion

762

(9)

Arc Length and the Unit Tangent Vector T

771

(5)

Curvature, Torsion, and the TNB Frame

776

(12)

Planetary Motion and Satellites

788

(11)

For Your Review

795

(1)

Practice Exercises

795

(4)

Partial Derivatives

Overview

799

(1)

Functions of Several Independent Variables

799

(9)

Limits and Continuity

808

(6)

Partial Derivatives

814

(9)

Differentiability, Linearization, and Differentials

823

(10)

The Chain Rule

833

(8)

Directional Derivatives, Gradient Vectors, and Tangent Planes

841

(12)

Maxima, Minima, and Saddle Points

853

(11)

Lagrange Multipliers

864

(13)

For Your Review

873

(1)

Practice Exercises

873

(4)

Multiple Integrals

Overview

877

(1)

Double Integrals

877

(10)

Areas, Moments, and Centers of Mass

887

(6)

Double Integrals in Polar Form

893

(6)

Triple Integrals in Rectangular Coordinates

899

(7)

Masses and Moments in Three Dimensions

906

(4)

Triple Integrals in Cylindrical and Spherical Coordinates

910

(9)

Substitutions in Multiple Integrals

919

(12)

For Your Review

927

(1)

Practice Exercises

927

(4)

Integration in Vector Fields

Overview

931

(1)

Line Integrals

931

(6)

Vector Fields, Work, Circulation, and Flux

937

(9)

Path Independence, Potential Functions, and Conservative Fields

946

(8)

Green's Theorem in the Plane

954

(11)

Surface Area and Surface Integrals

965

(10)

Parametrized Surfaces

975

(8)

Stokes's Theorem

983

(10)

The Divergence Theorem

993

For Your Review

1001

(1)

Practice Exercises

1001

Appendices

A.1 Formulas from Precalculus Mathematics

A-1

(1)

A.2 Proofs of the Limit Theorems in Chapter 2

A-6

(1)

A.3 A Proof of the Chain Rule for Functions of a Single Variable

A-9

(1)

A.4 Mathematical Induction

A-10

(1)

A.5 Simpson's One-Third Rule

A-13

(1)

A.6 Limits That Arise Frequently

A-14

(1)

A.7 Determinants and Cramer's Rule

A-16

(1)

A.8 Path Independence of ∫ F. dr Implies F = ∇f

A-24

(1)

A.9 Complex Numbers

A-25

(1)

A.10 Tables for sin x, cos x, tan x, ex, e--x, and ln x

A-26

(1)

Answers

A-29

(1)

Index

I-1

(1)

A Brief Table of Integrals

T-1

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Calculus

Summary

Table of Contents

Supplemental Materials