9780134437774

Calculus & Its Applications

David C. Lay, David I. Schneider, Larry J. Goldstein, Nakhlé H. Asmar

14th Edition

For one- or two-semester courses in Calculus for students majoring in business, social sciences, and life sciences. Intuition before Formality Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite int

0.1

Functions and Their Graphs

Exercises

p.9

0.2

Some Important Functions

Exercises

p.18

0.3

The Algebra of Functions

Exercises

p.23

0.4

Zeros of Functions - The Quadratic Formula and Factoring

Exercises

p.31

0.5

Exponents and Power Functions

Exercises

p.39

0.6

Functions and Graphs in Applications

Exercises

p.47

Fundamental Concept Check Exercises

p.54

Review Exercises

p.54

1.1

The Slope of a Straight Line

Exercises

p.63

1.2

The Slope of a Curve at a Point

Exercises

p.69

1.3

The Derivative and Limits

Exercises

p.79

1.4

Limits and the Derivative

Exercises

p.89

1.5

Differentiability and Continuity

Exercises

p.96

1.6

Some Rules for Differentiation

Exercises

p.102

1.7

More about Derivatives

Exercises

p.110

1.8

The Derivative as a Rate of Change

Exercises

p.119

Fundamental Concept Check Exercises

p.128

Review Exercises

p.129

2.1

Describing Graphs of Functions

Exercises

p.138

2.2

The First- and Second-Derivative Rules

Exercises

p.145

2.3

The First- and Second-Derivative Tests and Curve Sketching

Exercises

p.156

2.4

Curve Sketching (Conclusion)

Exercises

p.162

2.5

Optimization Problems

Exercises

p.168

2.6

Further Optimization Problems

Exercises

p.175

2.7

Applications of Derivatives to Business and Economics

Exercises

p.183

Fundamental Concept Check Exercises

p.189

Review Exercises

p.190

4.1

Exponential Functions

Exercises

p.225

4.2

The Exponential Function ex

Exercises

p.231

4.3

Differentiation of Exponential Functions

Exercises

p.235

4.4

The Natural Logarithm Function

Exercises

p.240

4.5

The Derivative of ln x

Exercises

p.244

4.6

Properties of the Natural Logarithm Function

Exercises

p.248

Fundamental Concept Check Exercises

p.251

Review Exercises

p.252

6.1

Antidifferentiation

Exercises

p.299

6.2

The Definite Integral and Net Change of a Function

Exercises

p.307

6.3

The Definite Integral and Area under a Graph

Exercises

p.317

6.4

Areas in the xy-Plane

Exercises

p.329

6.5

Applications of the Definite Integral

Exercises

p.338

Fundamental Concept Check Exercises

p.344

Review Exercises

p.344

7.1

Examples of Functions of Several Variables

Exercises

p.352

7.2

Partial Derivatives

Exercises

p.361

7.3

Maxima and Minima of Functions of Several Variables

Exercises

p.368

7.4

Lagrange Multipliers and Constrained Optimization

Exercises

p.376

7.5

The Method of Least Squares

Exercises

p.383

7.6

Double Integrals

Exercises

p.388

Fundamental Concept Check Exercises

p.392

Review Exercises

p.392

9.1

Integration by Substitution

Exercises

p.426

9.2

Integration by Parts

Exercises

p.430

9.3

Evaluation of Definite Integrals

Exercises

p.434

9.4

Approximation of Definite Integrals

Exercises

p.441

9.5

Some Applications of the Integral

Exercises

p.448

9.6

Improper Integrals

Exercises

p.452

Fundamental Concept Check Exercises

p.458

Review Exercises

p.459

10.1

Solutions of Differential Equations

Exercises

p.466

10.2

Separation of Variables

Exercises

p.473

10.3

First-Order Linear Differential Equations

Exercises

p.478

10.4

Applications of First-Order Linear Differential Equations

Exercises

p.483

10.5

Graphing Solutions of Differential Equations

Exercises

p.492

10.6

Applications of Differential Equations

Exercises

p.498

10.7

Numerical Solution of Differential Equations

Exercises

p.504

Fundamental Concept Check Exercises

p.510

Review Exercises

p.510

12.1

Discrete Random Variables

Exercises

p.557

12.2

Continuous Random Variables

Exercises

p.564

12.3

Expected Value and Variance

Exercises

p.569

12.4

Exponential and Normal Random Variables

Exercises

p.577

12.5

Poisson and Geometric Random Variables

Exercises

p.584

Fundamental Concept Check Exercises

p.588

Review Exercises

p.588