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

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

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

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)

Table of Contents

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 5.1 Hunting License Fees
    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
  • Answers to Odd Activities
  • 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
    Answers to Appendix A
  • 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
    Exponents and Radicals
    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
    Answers to Appendix B
    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
    Answers to Appendix C
    Solutions to Appendix C

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