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

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2004 Hard cover 3rd ed. Annotated. New. Sewn binding. Cloth over boards. 720 p.

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More About This Textbook

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.
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Product Details

  • ISBN-13: 9780618401284
  • Publisher: Cengage Learning
  • Publication date: 2/4/2004
  • Edition description: Older Edition
  • Edition number: 3
  • 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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