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Calculus and Its Applications

by: Larry J. Goldstein; David I. Schneider; David Caldwell Lay

Calculus and Its Applications

by: Larry J. Goldstein; David I. Schneider; David Caldwell Lay

ISBN 13:
9780130797667
ISBN 10:
0130797669
Edition: 8th
Format: Hardcover
Copyright: 12/01/1998
Publisher: Prentice Hall, Inc.
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Summary

This is the best-selling applied calculus text for the 4 year marketplace. More rigorous than Barnett, Goldstein/Lay/Schneider still provides an accessible text to students and instructor's alike. Integrating more usage of Excel and Optional Graphing calculator examples and exercises, this revision is sure to bring this classic to the classroom in an up-to-date approach. A full website with Excel sownloadable projects/tutuorials accompanies the text.

Perface

Introduction

(2)

0 Functions

(58)

0.1 Functions and Their Graphs

(15)

0.2 Some Important Functions

(9)

0.3 The Algebra of Functions

(4)

0.4 Zeros of Functions--The Quadratic Formula and Factoring

(9)

0.5 Exponents and Power Functions

(7)

0.6 Functions and Graphs in Applications

(14)

1 The Derivative

(70)

1.1 The Slope of a Straight Line

(10)

1.2 The Slope of a Curve at a Point

(6)

1.3 The Derivative

(9)

1.4 Limits and the Derivative

(11)

1.5 Differentiability and Continuity

(5)

1.6 Some Rules for Differentiation

103

(7)

1.7 More About Derivatives

110

(5)

1.8 The Derivative as a Rate of Change

115

(16)

2 Applications of the Derivative

131

(72)

2.1 Describing Graphs of Functions

131

(13)

2.2 The First and Second Derivative Rules

144

(10)

2.3 Curve Sketching (Introduction)

154

(8)

2.4 Curve Sketching (Conclusion)

162

(7)

2.5 Optimization Problems

169

(9)

2.6 Further Optimization Problems

178

(9)

*2.7 Applications of Calculus to Business and Economics

187

(16)

3 Techniques of Differentiation

203

(28)

3.1 The Product and Quotient Rules

203

(8)

3.2 The Chain Rule and the General Power Rule

211

(6)

3.3 Implicit Differentiation and Related Rates

217

(14)

4 The Exponential and Natural Logarithm Functions

231

(30)

4.1 Exponential Functions

231

(4)

4.2 The Exponential Function e(x)

235

(6)

4.3 Differentiation of Exponential Functions

241

(5)

4.4 The Natural Logarithm Function

246

(5)

4.5 The Derivative of In x

251

(4)

4.6 Properties of the Natural Logarithm Function

255

(6)

5 Applications of the Exponential and Natural Logarithm Functions

261

(40)

5.1 Exponential Growth and Decay

262

(10)

5.2 Compound Interest

272

(8)

*5.3 Applications of the Natural Logarithm Function to Economics

280

(6)

*5.4 Further Exponential Models

286

(15)

6 The Definite Integral

301

(56)

6.1 Antidifferentiation

302

(9)

6.2 Areas and Riemann Sums

311

(10)

6.3 Definite Integrals and the Fundamental Theorem

321

(11)

6.4 Areas in the xy-Plane

332

(10)

6.5 Applications of the Definite Integral

342

(15)

7 Functions of Several Variables

357

(54)

7.1 Examples of Functions of Several Variables

357

(7)

7.2 Partial Derivatives

364

(11)

7.3 Maxima and Minima of Functions of Several Variables

375

(8)

7.4 Lagrange Multipliers and Constrained Optimization

383

(11)

*7.5 The Method of Least Squares

394

(7)

*7.6 Double Integrals

401

(10)

8 The Trigonometric Functions

411

(32)

8.1 Radian Measure of Angles

411

(4)

8.2 The Sine and the Cosine

415

(9)

8.3 Differentiation of sin t and cost

424

(10)

8.4 The Tangent and Other Trigonometric Functions

434

(9)

9 Techniques of Integration

443

(46)

9.1 Integration by Substitution

445

(6)

9.2 Integration by Parts

451

(5)

9.3 Evaluation of Definite Integrals

456

(5)

*9.4 Approximation of Definite Integrals

461

(12)

*9.5 Some Applications of the Integral

473

(5)

9.6 Improper Integrals

478

(11)

10 Differential Equations

489

(46)

10.1 Solutions of Differential Equations

489

(7)

*10.2 Separation of Variables

496

(9)

*10.3 Numerical Solution of Differential Equations

505

(7)

10.4 Qualitative Theory of Differential Equations

512

(10)

10.5 Applications of Differential Equations

522

(13)

11 Taylor Polynomials and Infinite Series

535

(46)

11.1 Taylor Polynomials

535

(9)

*11.2 The Newton-Raphson Algorithm

544

(9)

11.3 Infinite Series

553

(10)

*11.4 Series with Positive Terms

563

(7)

11.5 Taylor Series

570

(11)

12 Probability and Calculus

581

12.1 Discrete Random Variables

581

(8)

12.2 Continuous Random Variables

589

(10)

12.3 Expected Value and Variance

599

(6)

12.4 Exponential and Normal Random Variables

605

(11)

12.5 Poisson and Geometric Random Variables

616

Appendices

A Calculus and the TI-82 Calculator

B Calculus and the TI-83 Calculator

C Calculus and the TI-85 Calculator

A11

D Calculus and the TI-86 Calculator

A16

E Areas Under the Standard Normal Curve

A22

Answers to Exercises

A23

Index

*Sections preceded by a * are optional in the sense that they are not prerequisites for later material.

Amazon no longer offers textbook rentals. We do!

Calculus and Its Applications

Calculus and Its Applications

9780130797667

0130797669

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Calculus and Its Applications

Calculus and Its Applications

9780130797667

0130797669

Summary

Table of Contents

Supplemental Materials

Write a Review

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