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Calculus Concepts An Informal Approach to the Mathematics of Change, Brief

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

Calculus Concepts An Informal Approach to the Mathematics of Change, Brief

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

ISBN 13:
9780618401277
ISBN 10:
061840127X
Edition: 3rd
Format: Hardcover
Copyright: 02/04/2004
Publisher: Brooks Cole
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Summary

For full description, see catalog entry for La Torre et al.,Calculus Concepts,3/e.

To Students

xiii

Preface

Ingredients of Change: Functions and Linear Models

(74)

Models, Functions, and Graphs

(15)

Mathematical Models

(2)

Functions

(1)

Determining Outputs

(1)

Units of Measure

(1)

Graphically Recognizing Functions

(2)

Modeling in Business

(2)

Concept Inventory

(1)

Activities

(5)

Constructed Functions

(15)

Combining Functions

(6)

Piecewise Continuous Functions

(1)

Inverse Functions

(4)

Concept Inventory

(1)

Activities

(4)

Functions, Limits, and Continuity

(16)

Limits and the Infinitely Large

(2)

Limits and the Infinitesimally Small

(3)

Continuity

(2)

Continuity and Function Interpretation

(1)

Functions That Are Continuous without Restriction

(2)

A Financial Illustration of Continuity, Interpretation, and a Limit

(1)

Concept Inventory

(1)

Activities

(4)

Linear Functions and Models

(26)

Representations of a Linear Model

(1)

The Parameters of a Linear Model: Slope and Intercept

(3)

Finding a Linear Model from Data

(3)

Aligning Data

(2)

What Is ``Best Fit''?

(1)

Numerical Considerations: Reporting Answers

(1)

Numerical Considerations: Calculating Answers

(1)

The Four Elements of a Model

(1)

Concept Inventory

(1)

Activities

(6)

Summary

(1)

Concept Check

(1)

Review Test

(2)

Tuition Fees

(1)

United States Population

(1)

Ingredients of Change: Nonlinear Models

(80)

Exponential Functions and Models

(13)

Percentage Change and Exponential Models

(1)

Percentage Differences from Data

(2)

Finding Exponential Models

(2)

Doubling Time and Half-Life

(2)

Numerical Considerations

(1)

Concept Inventory

(1)

Activities

(4)

Logarithmic Functions and Models

(10)

Logarithmic Models

(3)

Aligning Log Data

(2)

An Important Inverse Relationship

(1)

Concept Inventory

(1)

Activities

(4)

Logistic Functions and Models

101

(16)

Exponential Growth with Constraints

101

(2)

Finding Logistic Models

103

(4)

Shifting Logistic and Exponential Data

107

(4)

Concept Inventory

111

(1)

Activities

111

(6)

Polynomial Functions and Models

117

(19)

Quadratic Modeling

118

(4)

Quadratic or Exponential?

122

(2)

Cubic Modeling

124

(5)

Concept Inventory

129

(1)

Activities

129

(7)

Choosing a Function to Fit Data

136

(20)

Shifting Data

136

(1)

Examining Scatter Plots

137

(3)

The Steps in Choosing a Model

140

(4)

Concept Inventory

144

(1)

Activities

144

(4)

Summary

148

(1)

Concept Check

149

(1)

Review Test

150

(2)

Compulsory School Laws

152

(2)

Fund-Raising Campaign

154

(2)

Describing Change: Rates

156

(76)

Change, Percentage Change, and Average Rates of Change

158

(15)

Interpreting Descriptions of Change

159

(2)

Finding Percentage Change and Average Rate of Change Using Graphs

161

(4)

Determining Percentage Change and Average Rate of Change Using an Equation

165

(2)

Concept Inventory

167

(1)

Activities

167

(6)

Instantaneous Rates of Change

173

(18)

Local Linearity and Tangent Lines

174

(3)

Secant and Tangent Lines

177

(1)

Sketching Tangent Lines

178

(2)

Where Does the Instantaneous Rate of Change Exist?

180

(2)

Approximating Instantaneous Rates of Change

182

(2)

Concept Inventory

184

(1)

Activities

184

(7)

Derivatives

191

(15)

Derivative Terminology and Notation

191

(2)

Interpreting Derivatives

193

(3)

Approximating with Derivatives

196

(2)

Does Instantaneous Refer to Time?

198

(1)

Percentage Rate of Change

199

(2)

Concept Inventory

201

(1)

Activities

201

(5)

Numerically Finding Slopes

206

(11)

Finding Slopes by the Numerical Method

206

(4)

Finding Slopes of Piecewise Functions

210

(2)

Concept Inventory

212

(1)

Activities

213

(4)

Algebraically Finding Slopes

217

(15)

Finding Slopes Using the Algebraic Method

217

(3)

A General Formula for Derivatives

220

(4)

Concept Inventory

224

(1)

Activities

224

(2)

Summary

226

(1)

Concept Check

227

(1)

Review Test

228

(2)

Fee-Refund Schedules

230

(1)

Doubling Time

231

(1)

Determining Change: Derivatives

232

(64)

Drawing Rate-of-Change Graphs

234

(14)

Extracting Rate-of-Change Information from a Function Graph

234

(4)

A Detailed Look at the Slope Graph

238

(3)

Points of Undefined Slope

241

(2)

Concept Inventory

243

(1)

Activities

243

(5)

Simple Rate-of-Change Formulas

248

(13)

The Simple Power Rule

248

(1)

The Constant Multiplier and Sum and Difference Rules

249

(5)

Derivatives of Piecewise Functions

254

(2)

Concept Inventory

256

(1)

Activities

256

(5)

More Simple Rate-of-Change Formulas

261

(10)

Exponential Rules

261

(3)

Natural Logarithm Rule

264

(3)

Concept Inventory

267

(1)

Activities

267

(4)

The Chain Rule

271

(9)

The First Form of the Chain Rule

271

(2)

The Second Form of the Chain Rule

273

(3)

Concept Inventory

276

(1)

Activities

276

(4)

The Product Rule

280

(16)

Applying the Product Rule without Equations

281

(2)

Applying the Product Rule with Equations

283

(2)

The Quotient Rule

285

(1)

Concept Inventory

285

(1)

Activities

285

(6)

Summary

291

(1)

Concept Check

292

(1)

Review Test

292

(2)

Superhighway

294

(1)

Fertility Rates

295

(1)

Analyzing Change: Applications of Derivatives

296

Approximating Change

298

Using Rates of Change to Approximate Change

298

Marginal Analysis

303

Concept Inventory

306

Activities

306

Relative and Absolute Extreme Points

311

Relative Extrema

311

Conditions When Relative Extrema Might Not Exist

315

Relative Extrema on Functions That Are Not Smooth

318

Absolute Extrema

319

Concept Inventory

322

Activities

322

Inflection Points

327

The Second Derivative

327

Concavity and the Second Derivative

333

Concept Inventory

334

Activities

334

Derivatives in Action

341

Concept Inventory

348

Activities

348

Interconnected Change: Related Rates

353

Concept Inventory

358

Activities

358

Summary

361

Concept Check

362

Review Test

362

Hunting License Fees

364

Fund-Raising Campaign

365

Amazon no longer offers textbook rentals. We do!

Calculus Concepts An Informal Approach to the Mathematics of Change, Brief

Calculus Concepts An Informal Approach to the Mathematics of Change, Brief

9780618401277

061840127X

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Calculus Concepts An Informal Approach to the Mathematics of Change, Brief

Calculus Concepts An Informal Approach to the Mathematics of Change, Brief

9780618401277

061840127X

Summary

Table of Contents

Supplemental Materials

Write a Review

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