# Calculus Concepts: An Informal Approach to Mathematics of Change / Edition 3

ISBN-10: 0618401288

ISBN-13: 9780618401284

Pub. Date: 02/04/2004

Publisher: Cengage Learning

Designed for the one- to two-semester business/applied calculus course that commonly requires the use of graphing calculators and spreadsheets, this text uses applications and technology to develop concepts before presenting concrete examples. The text presents the mathematics using many representations—algebraic, graphical, numeric, and verbal—to help

## Overview

Designed for the one- to two-semester business/applied calculus course that commonly requires the use of graphing calculators and spreadsheets, this text uses applications and technology to develop concepts before presenting concrete examples. The text presents the mathematics using many representations—algebraic, graphical, numeric, and verbal—to help students of diverse learning styles better understand and connect concepts. Students also use real data and graphing technology to build models and interpret results.

## Product Details

ISBN-13:
9780618401284
Publisher:
Cengage Learning
Publication date:
02/04/2004
Edition description:
Older Edition
Pages:
720
Product dimensions:
8.34(w) x 10.06(h) x 1.37(d)

Contents

Note: Each chapter contains a Summary, a Concept Check, and a Review Test.

• 1. Ingredients of Change: Functions and Linear Models
1.1 Models, Functions, and Graphs
1.2 Constructed Functions
1.3 Functions, Limits, and Continuity
1.4 Linear Functions and Models
Project 1.1 Tuition Fees
Project 1.2 United States Population
• 2. Ingredients of Change: Nonlinear Models
2.1 Exponential Functions and Models
2.2 Logarithmic Functions and Models
2.3 Logistic Functions and Models
2.4 Polynomial Functions and Models
2.5 Choosing a Function to Fit Data
Project 2.1 Compulsory School Laws
Project 2.2 Fund-Raising Campaign
• 3. Describing Change: Rates
3.1 Change, Percentage Change, and Average Rates of Change
3.2 Instantaneous Rates of Change
3.3 Derivatives
3.4 Numerically Finding Slopes
3.5 Algebraically Finding Slopes
Project 3.1 Fee-Refund Schedules
Project 3.2 Doubling Time
• 4. Determining Change: Derivatives
4.1 Drawing Rate-of-Change Graphs
4.2 Simple Rate-of-Change Formulas
4.3 More Simple Rate-of-Change Formulas
4.4 The Chain Rule
4.5 The Product Rule
Project 4.1 Superhighway
Project 4.2 Fertility Rates
• 5. Analyzing Change: Applications of Derivatives
5.1 Approximating Change
5.2 Relative and Absolute Extreme Points
5.3 Inflection Points
5.4 Derivatives in Action
5.5 Interconnected Change: Related Rates
Project 5.2 Fund-Raising Campaign
• 6. Accumulating Change: Limits of Sums and the Definite Integral
6.1 Results of Change and AreaApproximations
6.2 Limit of Sums, Accumulated Change, and the Definite Integral
6.3 Accumulation Functions
6.4 The Fundamental Theorem
6.5 The Definite Integral
6.6 Average Value and Average Rate of Change
6.7 Antiderivative Limitations
Project 6.1 Acceleration, Velocity, and Distance
Project 6.2 Estimating Growth
• 7. Analyzing Accumulated Change: Integrals in Action
7.1 Perpetual Accumulation and Improper Integrals
7.2 Streams in Business and Biology
7.3 Integrals in Economics
7.4 Probability Distributions and Density Functions
Project 7.1 Arch Art
• 8. Repetitive Change: Cycles and Trigonometry
8.1 Functions of Angles: Sine and Cosine
8.2 Cyclic Functions as Models
8.3 Rates of Change and Derivatives
8.4 Extrema and Points of Inflection
8.5 Accumulation in Cycles
Project 8.1 Seasonal Sales
Project 8.2 Lake Tahoe Levels
• 9. Ingredients of Multivariable Change: Models, Graphs, Rates
9.1 Multivariable Functions and Contour Graphs
9.2 Cross-Sectional Models and Rates of Change
9.3 Partial Rates of Change
9.4 Compensating for Change
Project 9.1 Competitive and Complementary Products
Project 9.2 Expert Witness
• 10. Analyzing Multivariable Change: Optimization
10.1 Multivariable Critical Points
10.2 Multivariable Optimization
10.3 Optimization Under Constraints
10.4 Least-Squares Optimization
Project 10.1 Snow Cover
Project 10.2 Carbonated Beverage Packaging
• Index of Applications
• Subject Index
• Chapter 11 and the Appendices are available via the Internet.
• 11. Dynamics of Change: Differential Equations and Proportionality
11.1 Differential Equations and Slope Fields
11.2 Separable Differential Equations
11.3 Numerically Estimating by Using Differential Equations: Euler's Method
11.4 Second-Order Differential Equations
Chapter 11 Answers to Odd Activities
• Appendix A: Trigonometry Basics
Trigonometry Basics
• Appendix B: Strengthening the Concepts
The Pythagorean Theorem
Solving Exponential Equations Algebraically
Graphing Piecewise Functions
Constructing Inverse Functions Algebraically
Determining End Behavior Algebraically
The Limit at a Point
Polynomial and Rational Functions
Continuity Defined
APR and APY
Squaring and Cubing Binomials
The Constant Multiplier and Sum Rules for Derivatives
Negative and Fractional Exponents
Formulas for Geometry-Related Problems
Solving Systems of Equations Algebraically
Solutions to Appendix B
• Appendix C: Strengthening the Skills
1.1 Skill Strengthening
4.2 Skill Strengthening
4.3 Skill Strengthening
4.4 Skill Strengthening
4.5 Skill Strengthening
6.4 Skill Strengthening