Thomas' Calculus, Updated

by: Thomas, George B.; Finney, Ross L.; Weir, Jan D.; Giordano

Thomas' Calculus, Updated

by: Thomas, George B.; Finney, Ross L.; Weir, Jan D.; Giordano

ISBN 13:
9780201755275
ISBN 10:
0201755270
Edition: 10th
Format: Package
Copyright: 01/01/2003
Publisher: Addison Wesley

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Summary

The updated tenth edition of this clear, precise calculus text with superior applications sets the standard in calculus. This proven text was carefully revised to give students the solid base they need to succeed in math, science and engineering programs. Through a comprehensive technology package, this edition now includes more opportunity to incorporate optional, but meaningful, technology into the course.

To the Instructor

xiii

To the Student

xxv

P Preliminaries

(1142)

Lines

(9)

Functions and Graphs

(14)

Exponential Functions

(7)

Inverse Functions and Logarithms

(13)

Trigonometric Functions and Their Inverses

(16)

Parametric Equations

(7)

Modeling Change

(18)

Questions to Guide Your Review

(1)

Practice Exercises

(3)

Additional Exercises: Theory, Examples, applications

(5)

Limits and Continuity

(62)

Rates of Change and Limits

(14)

Finding Limits and One-Sided Limits

(13)

Limits Involving Infinity

112

(11)

Continuity

123

(11)

Tangent Lines

134

(13)

Questions to Guide Your Review

141

(1)

Practice Exercises

142

(1)

Additional Exercises: Theory, Examples, Applications

143

(4)

Derivatives

147

(78)

The Derivative as a Function

147

(13)

The Derivative as a Rate of Change

160

(13)

Derivatives of Products, Quotients, and Negative Powers

173

(6)

Derivatives of Trigonometric Functions

179

(8)

The Chain Rule and Parametric Equations

187

(11)

Implicit Differentiation

198

(9)

Related Rates

207

(18)

Questions To Guide Your Review

216

(1)

Practice Exercises

217

(4)

Additional Exercises: Theory, Examples, Applications

221

(4)

Applications of Derivatives

225

(88)

Extreme Values of Functions

225

(12)

The Mean Value Theorem and Differential Equations

237

(8)

The Shape of a Graph

245

(12)

Graphical Solutions of Autonomous Differential Equations

257

(9)

Modeling and Optimization

266

(17)

Linearization and Differentials

283

(14)

Newton's Method

297

(16)

Questions to Guide Your Review

305

(1)

Practice Exercises

305

(4)

Additional Exercises: Theory, Examples, Applications

309

(4)

Integration

313

(80)

Indefinite Integrals, Differential Equations, and Modeling

313

(9)

Integral Rules; Integration by Substitution

322

(7)

Estimating with Finite Sums

329

(11)

Riemann Sums and Definite Integrals

340

(11)

The Mean Value and Fundamental Theorems

351

(13)

Substitution in Definite Integrals

364

(9)

Numerical Integration

373

(20)

Questions to Guide Your Review

384

(1)

Practice Exercises

385

(4)

Additional Exercises: Theory, Examples, Applications

389

(4)

Applications of Integrals

393

(64)

Volumes by Slicing and Rotation About an Axis

393

(13)

Modeling Volume Using Cylindrical Shells

406

(7)

Lengths of Plane Curves

413

(8)

Springs, Pumping, and Lifting

421

(11)

Fluid Forces

432

(7)

Moments and Centers of Mass

439

(18)

Questions to Guide Your Review

451

(1)

Practice Exercises

451

(3)

Additional Exercises: Theory, Examples, Applications

454

(3)

Transcendental Functions and Differential Equations

457

(82)

Logarithms

457

(9)

Exponential Functions

466

(11)

Derivatives of Inverse Trigonometric Functions; Integrals

477

(8)

First-Order Separable Differential Equations

485

(14)

Linear First-Order Differential Equations

499

(8)

Euler's Method; Population Models

507

(13)

Hyperbolic Functions

520

(19)

Questions to Guide Your Review

530

(1)

Practice Exercises

531

(4)

Additional Exercises: Theory, Examples, Applications

535

(4)

Integration Techniques, L'Hopital's Rule, and Improper Integrals

539

(68)

Basic Integration Formulas

539

(7)

Integration by Parts

546

(9)

Partial Fractions

555

(10)

Trigonometric Substitutions

565

(5)

Integral Tables, Computer Algebra Systems, and Monte Carlo Integration

570

(8)

L'Hopital's Rule

578

(8)

Improper Integrals

586

(21)

Questions to Guide Your Review

600

(1)

Practice Exercises

601

(2)

Additional Exercises: Theory, Examples, Applications

603

(4)

Infinite Series

607

(110)

Limits of Sequences of Numbers

608

(11)

Subsequences, Bounded Sequences, and Picard's Method

619

(8)

Infinite Series

627

(12)

Series of Nonnegative Terms

639

(12)

Alternating Series, Absolute and Conditional Convergence

651

(9)

Power Series

660

(9)

Taylor and Maclaurin Series

669

(14)

Applications of Power Series

683

(8)

Fourier Series

691

(7)

Fourier Cosine and Sine Series

698

(19)

Questions to Guide Your Review

707

(1)

Practice Exercises

708

(3)

Additional Exercises: Theory, Examples, Applications

711

(6)

Vectors in the Plane and Polar Functions

717

(70)

Vectors in the Plane

717

(11)

Dot Products

728

(10)

Vector-Valued Functions

738

(11)

Modeling Projectile Motion

749

(12)

Polar Coordinates and Graphs

761

(9)

Calculus of Polar Curves

770

(17)

Questions to Guide Your Review

780

(1)

Practice Exercises

780

(4)

Additional Exercises: Theory, Examples, Applications

784

(3)

Vectors and Motion in Space

787

(86)

Cartesian (Rectangular) Coordinates and Vectors in Space

787

(9)

Dot and Cross Products

796

(11)

Lines and Planes in Space

807

(9)

Cylinders and Quadric Surfaces

816

(9)

Vector-Valued Functions and Space Curves

825

(13)

Arc Length and the Unit Tangent Vector T

838

(9)

The TNB Frame; Tangential and Normal Components of Acceleration

847

(10)

Planetary Motion and Satellites

857

(16)

Questions to Guide Your Review

866

(1)

Practice Exercises

867

(3)

Additional Exercises: Theory, Examples, Applications

870

(3)

Multivariable Functions and Their Derivatives

873

(102)

Functions of Several Variables

873

(9)

Limits and Continuity in Higher Dimensions

882

(8)

Partial Derivatives

890

(12)

The Chain Rule

902

(9)

Directional Derivatives, Gradient Vectors, and Tangent Planes

911

(14)

Linearization and Differentials

925

(11)

Extreme Values and Saddle Points

936

(11)

Lagrange Multipliers

947

(11)

*Partial Derivatives with Constrained Variables

958

(5)

Taylor's Formula for Two Variables

963

(12)

Questions to Guide Your Review

968

(1)

Practice Exercises

968

(4)

Additional Exercises: Theory, Examples, Applications

972

(3)

Multiple Integrals

975

(78)

Double Integrals

975

(12)

Areas, Moments and Centers of Mass*

987

(13)

Double Integrals in Polar Form

1000

(7)

Triple Integrals in Rectangular Coordinates

1007

(10)

Masses and Moments in Three Dimensions

1017

(7)

Triple Integrals in Cylindrical and Spherical Coordinates

1024

(13)

Substitutions in Multiple Integrals

1037

(16)

Questions to Guide Your Review

1046

(1)

Practice Exercises

1047

(2)

Additional Exercises: Theory, Examples, Applications

1049

(4)

Integration in Vector Fields

1053

(90)

Line Integrals

1053

(6)

Vector Fields, Work, Circulation, and Flux

1059

(11)

Path Independence, Potential Functions and Conservative Fields

1070

(10)

Green's Theorem in the Plane

1080

(12)

Surface Area and Surface Integrals

1092

(11)

Parametrized Surfaces

1103

(10)

Stokes' Theorem

1113

(11)

Divergence Theorem and a Unified Theory

1124

(19)

Questions to Guide Your Review

1136

(1)

Practice Exercises

1136

(3)

Additional Exercises: Theory, Examples, Applications

1139

(4)

Appendices

1143

A.1 Mathematical Induction

1143

(3)

A.2 Proofs of Limit Theorems in Section 1.2

1146

(4)

A.3 Proof of the Chain Rule

1150

(1)

A.4 Complex Numbers

1151

(11)

A.5 Simpson's One-Third Rule

1162

(1)

A.6 Cauchy's Mean Value Theorem and the Stronger Form of L'Hopital's Rule

1163

(1)

A.7 Limits That Arise Frequently

1164

(2)

A.8 Proof of Taylor's Theorem

1166

(1)

A.9 The Distributive Law for Vector Cross Products

1167

(2)

A.10 Determinants and Cramer's Rule

1169

(7)

A.11 The Mixed Derivative Theorem and the Increment Theorem

1176

(5)

A.12 The Area of a Parallelogram's Projection on a Plane

1181

(2)

A.13 Conic Sections

1183

Answers

(1)

Index

(1)

A Brief Table of Integrals

Thomas' Calculus, Updated

Thomas' Calculus, Updated

9780201755275

0201755270

Summary

Table of Contents

Supplemental Materials

Write a Review

Thomas' Calculus, Updated

Thomas' Calculus, Updated

9780201755275

0201755270

Summary

Table of Contents

Supplemental Materials

Write a Review

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