9781439049570

Calculus Concepts: An Informal Approach to the Mathematics of Change

Cynthia R. Harris, Donald R. LaTorre, Iris B. Reed, John W. Kenelly, Laurel R. Carpenter

5th Edition

This innovative text features a graphing calculator approach, incorporating real-life applications and such technology as graphing utilities and Excel spreadsheets to help students learn mathematical skills that they will use in their lives and careers. The texts overall goal is to improve learning of basic calculus concepts by involving students with new material in a way

1-1

Functions-Four Representation

Activities

p.9

1-2

Function Behavior and End Behavior Limits

Activities

p.19

1-3

Limits and Continuity

Activities

p.30

1-4

Linear Functions and Models

Activities

p.42

1-5

Exponential Functions and Models

Activities

p.53

1-6

Models in France

Activities

p.64

1-7

Constructed Functions

Activities

p.72

1-8

Logarithmic Functions and Models

Activities

p.81

1-9

Quadratic Functions and Models

Activities

p.91

1-10

Logistic Functions and Models

Activities

p.98

1-11

Cubic Functions and Models

Activities

p.107

1-12

Cyclic Functions and Models

Activities

p.115

Review Activities

p.122

2-1

Measures of Change Over an Interval

Activities

p.134

2-2

Measures of Change at a Point-Graphical

Activities

p.147

2-3

Rates of Change-Notation and Interpretation

Activities

p.157

2-4

Rates of Change-Numerical Limits and Nonexistence

Activities

p.163

2-5

Rates of Change Defined over Intervals

Activities

p.172

2-6

Rate-of-Change Graphs

Activities

p.180

Review Activities

p.185

3-1

Simple Rate-of-Change Formulas

Activities

p.198

3-2

Exponential, Logarithmic, and Cyclic Rate-or-Change Formulas

Activities

p.209

3-3

Rates of Change for Functions That Can Be Composed

Activities

p.216

3-4

Rates of Change of Composite Functions

Activities

p.223

3-5

Rates of Change for Functions That Can Be Multiplied

Activities

p.232

3-6

Rates of Change of Product Functions

Activities

p.237

3-7

Limits of Quotients and L'Hospital's Rule

Activities

p.244

Review Activities

p.246

4-1

Linearization and Estimates

Activities

p.254

4-2

Relative Extreme Points

Activities

p.264

4-3

Absolute Extreme Points

Activities

p.271

4-4

Inflection Points and Second Derivatives

Activities

p.280

4-5

Marginal Analysis

Activities

p.288

4-6

Optimization of Constructed Functions

Activities

p.298

4-7

Related Rates

Activities

p.309

Review Activities

p.313

5-1

An Introduction to Results of Change

Activities

p.324

5-2

Limits of Sums and the Definite Integral

Activities

p.338

5-3

Accumulating Functions

Activities

p.350

5-4

The Fundamental Theorem

Activities

p.363

5-5

Antiderivative Formulas for Exponential, Natural Log, and Sine Functions

Activities

p.373

5-6

The Definite Integral-Algebraically

Activities

p.381

5-7

Difference of Accumulated Change

Activities

p.389

5-8

Average Value and Average Rate of Change

Activities

p.399

5-9

Integration of Product or Composite Functions

Activities

p.409

Review Activities

p.411

6-1

Perpetual Accumulation and Improper Integrals

Activities

p.422

6-2

Streams in Business and Biology

Activities

p.435

6-3

Calculus in Economics-Demand and Elasticity

Activities

p.447

6-4

Calculus in Economics-Supply and Equilibrium

Activities

p.461

6-5

Calculus in Probability (Part 1)

Activities

p.472

6-6

Calculus in Probability (Part 2)

Activities

p.482

6-7

Differential Equations-Slope Fields and Solution

Activities

p.494

6-8

Differential Equations-Proportionality and Common Forms

Activities

p.507

Review Activities

p.514