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Thomas' Calculus

by: Thomas, George B.

Thomas' Calculus

by: Thomas, George B.

ISBN 13:
9780321117717
ISBN 10:
0321117719
Edition: Alternate
Format: Hardcover
Copyright: 03/01/2002
Publisher: Pearson College Div
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Summary

George Thomas' clear precise calculus text with superior applications defined the modern-day calculus course. This proven text gives students the solid base of material they will need to succeed in math, science, and engineering programs.

To the Instructor

viii

To the Student

xvii

P Preliminaries

Real Numbers and the Real Line

(7)

Coordinates, Lines, and Increments

(9)

Functions

(10)

Shifting Graphs

(8)

Trigonometric Functions

(16)

Questions to Guide Your Review

(1)

Practice Exercises

(1)

Additional Exercises-Theory, Examples, Applications

(2)

Limits and Continuity

Rates of Change and Limits

(10)

Rules for Finding Limits

(5)

Target Values and Formal Definitions of Limits

(12)

Extensions of the Limit Concept

(9)

Continuity

(10)

Tangent Lines

(12)

Questions to Guide Your Review

103

(1)

Practice Exercises

104

(1)

Additional Exercises-Theory, Examples, Applications

105

(4)

Derivatives

The Derivative of a Function

109

(12)

Differentiation Rules

121

(10)

Rates of Change

131

(12)

Derivatives of Trigonometric Functions

143

(11)

The Chain Rule

154

(10)

Implicit Differentiation and Rational Exponents

164

(8)

Related Rates of Change

172

(17)

Questions to Guide Your Review

180

(1)

Practice Exercises

181

(4)

Additional Exercises-Theory, Examples, Applications

185

(4)

Application of Derivatives

Extreme Values of Functions

189

(7)

The Mean Value Theorem

196

(9)

The First Derivative Test for Local Extreme Values

205

(4)

Graphing with y' and y''

209

(11)

Limits as x → ± ∞, Asymptotes, and Dominant Terms

220

(13)

Optimization

233

(15)

Linearization and Differentials

248

(12)

Newton's Method

260

(15)

Questions to Guide Your Review

268

(1)

Practice Exercises

269

(3)

Additional Exercises-Theory, Examples, Applications

272

(3)

Integration

Indefinite Integrals

275

(7)

Differential Equations, Initial Value Problems, and Mathematical Modeling

282

(8)

Integration by Substitution-Running the Chain Rule Backward

290

(8)

Estimating with Finite Sums

298

(11)

Riemann Sums and Definite Integrals

309

(14)

Properties, Area, and the Mean Value Theorem

323

(9)

The Fundamental Theorem

332

(10)

Substitution in Definite Integrals

342

(4)

Numerical Integration

346

(19)

Questions to Guide Your Review

356

(1)

Practice Exercises

357

(3)

Additional Exercises-Theory, Examples, Applications

360

(5)

Applications of Integrals

Areas Between Curves

365

(9)

Finding Volumes by Slicing

374

(5)

Volumes of Solids of Revolution-Disks and Washers

379

(8)

Cylindrical Shells

387

(6)

Lengths of Plane Curves

393

(7)

Areas of Surfaces of Revolution

400

(7)

Moments and Centers of Mass

407

(11)

Work

418

(9)

Fluid Pressures and Forces

427

(7)

The Basic Pattern and Other Modeling Applications

434

(15)

Questions to Guide Your Review

444

(1)

Practice Exercises

444

(3)

Additional Exercises-Theory, Examples, Applications

447

(2)

Transcendental Functions

Inverse Functions and Their Derivatives

449

(9)

Natural Logarithms

458

(9)

The Exponential Function

467

(7)

ax and logax

474

(8)

Growth and Decay

482

(9)

L'Hopital's Rule

491

(7)

Relative Rates of Growth

498

(6)

Inverse Trigonometric Functions

504

(9)

Derivatives of Inverse Trigonometric Functions; Integrals

513

(7)

Hyperbolic Functions

520

(9)

First Order Differential Equations

529

(12)

Euler's Numerical Method; Slope Fields

541

(14)

Questions to Guide Your Review

547

(1)

Practice Exercises

548

(3)

Additional Exercies-Theory, Examples, Applications

551

(4)

Techniques of Integration

Basic Integration Formulas

555

(7)

Integration by Parts

562

(7)

Partial Fractions

569

(9)

Trigonometric Substitutions

578

(5)

Integral Tables and CAS

583

(11)

Improper Integrals

594

(19)

Questions to Guide Your Review

606

(1)

Practice Exercises

606

(3)

Additional Exercises-Theory, Examples, Applications

609

(4)

Infinite Series

Limits of Sequences of Numbers

613

(9)

Theorems for Calculating Limits of Sequences

622

(8)

Infinite Series

630

(10)

The Integral Test for Series of Nonnegative Terms

640

(4)

Comparison Tests for Series of Nonnegative Terms

644

(5)

The Ratio and Root Tests for Series of Nonnegative Terms

649

(6)

Alternating Series, Absolute and Conditional Convergence

655

(8)

Power Series

663

(9)

Taylor and Maclaurin Series

672

(6)

Convergence of Taylor Series; Error Estimates

678

(10)

Applications of Power Series

688

(21)

Questions to Guide Your Review

699

(1)

Practice Exercises

700

(3)

Additional Exercises-Theory, Examples, Applications

703

(6)

Conic Sections, Parametrized Curves, and Polar Coordinates

Conic Section and Quadratic Equations

709

(14)

Classifying Conic Sections by Eccentricity

723

(5)

Quadratic Equations and Rotations

728

(6)

Parametrizations of Plane Curves

734

(10)

Calculus with Parametrized Curves

744

(7)

Polar Coordinates

751

(5)

Graphing in Polar Coordinates

756

(8)

Polar Equations for Conic Sections

764

(6)

Integration in Polar Coordinates

770

(17)

Questions to Guide Your Review

777

(1)

Practice Exercises

778

(5)

Additional Exercises-Theory, Examples, Applications

783

(4)

Vectors and Analytic Geometry in Space

Vectors in the Plane

787

(8)

Cartesian (Rectangular) Coordinates and Vectors in Space

795

(11)

Dot Products

806

(9)

Cross Products

815

(7)

Lines and Planes in Space

822

(7)

Cylinders and Quadric Surfaces

829

(12)

Cylindrical and Spherical Coordinates

841

(14)

Questions to Guide Your Review

847

(1)

Practice Exercises

848

(3)

Additional Exercises-Theory, Examples, Applications

851

(4)

Vector-Valued Functions and Motion in Space

Vector-Valued Functions and Space Curves

855

(13)

Modeling Projectile Motion

868

(8)

Arc Length and the Unit Tangent Vector T

876

(5)

Curvature, Torison, and the TNB Frame

881

(12)

Planetary Motion and Satellites

893

(16)

Questions to Guide Your Review

902

(1)

Practice Exercises

902

(3)

Additional Exercises-Theory, Examples, Application

905

(4)

Multivariable Functions and Partial Derivatives

Functions of Several Variables

909

(8)

Limits and Continuity

917

(7)

Partial Derivatives

924

(9)

Differentiability, Linearization, and Differentials

933

(11)

The Chain Rule

944

(8)

Partial Derivatives with Constrained Variables

952

(5)

Directional Derivatives, Gradient Vectors, and Tangent Planes

957

(13)

Extreme Values and Saddle Points

970

(10)

Lagrange Multipliers

980

(9)

Taylor's Formula

989

(12)

Questions to Guide Your Review

993

(1)

Practice Exercises

994

(4)

Additional Exercises-Theory, Examples, Applications

998

(3)

Multiple Integrals

Double Integrals

1001

(11)

Areas, Moments, and Centers of Mass

1012

(8)

Double Integrals in Polar Form

1020

(6)

Triple Integrals in Rectangular Coordinates

1026

(8)

Masses and Moments in Three Dimensions

1034

(5)

Triple Integrals in Cylindrical and Spherical Coordinates

1039

(9)

Substitutions in Multiple Integrals

1048

(13)

Questions to Guide Your Review

1055

(1)

Practice Exercises

1056

(2)

Additional Exercises-Theory, Examples, Applications

1058

(3)

Integration in Vector Fields

Line Integrals

1061

(6)

Vector Fields, Work, Circulation, and Flux

1067

(9)

Path Independence, Potential Functions, and Conservative Fields

1076

(8)

Green's Theorem in the Plane

1084

(12)

Surface Area and Surface Integrals

1096

(10)

Parametrized Surfaces

1106

(8)

Stokes's Theorem

1114

(9)

The Divergence Theorem and a Unified Theory

1123

Questions to Guide Your Review

1134

(1)

Practice Exercises

1134

(3)

Additional Exercises-Theory, Examples, Applications

1137

Appendices

A.1 Mathematical Induction

A-1

A.2 Proofs of Limit Theorems in Section 1.2

A-4

A.3 Complex Numbers

A-7

A.4 Simpson's One-Third Rule

A-17

A.5 Cauchy's Mean Value Theorem and the Stronger Form of I'Hopital's Rule

A-18

A.6 Limits That Arise Frequently

A-20

A.7 The Distributive Law for Vector Cross Products

A-21

A.8 Determinants and Cramer's Rule

A-22

A.9 Euler's Theorem and the Increment Theorem

A-29

Answers

A-35

Index

I-1

A Brief Table of Integrals

T-1

Amazon no longer offers textbook rentals. We do!

Thomas' Calculus

Thomas' Calculus

9780321117717

0321117719

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Thomas' Calculus

Thomas' Calculus

9780321117717

0321117719

Summary

Table of Contents

Supplemental Materials

Write a Review

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