Calculus Concepts An Informal Approach to the Mathematics of Change

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

• ISBN13: 9780618401284
• ISBN10: 0618401288
• Edition: 3rd
• Format: Hardcover
• Copyright: 2004-02-04
• Publisher: Brooks Cole

Summary

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. Diverse exercise sets give instructors a wide variety of exercise formats to choose from when creating homework assignments. An Activities Key found at the beginning of each exercise set in the Instructor's Annotated Edition labels the types of exercises. This approach enables students to learn when it is appropriate to use technology or when exercises involve such things as writing or critical thinking. A navigation icon appears next to places within the text where multiple representations of a mathematical concept are presented. By presenting topics algebraically, graphically, numerically, and verbally, students see the connections between the different formats. In addition, various learning styles are addressed, allowing a greater majority of students to understand the material. Spreadsheet and Graphing Calculator Activities are located throughout the text to help students visualize concepts and learn how to use these key technological tools. Projects may be assigned by instructors to allow students to strengthen their writing and presentation skills while they learn to communicate mathematically. Eduspace is Houghton Mifflin's online learning tool. Powered by Blackboard, Eduspace is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content. The LaTorre et al. Calculus Concepts course features algorithmic exercises, test bank content in question pools and video explanations.

Table of Contents

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

Ingredients of Change: Functions and Linear Models

Models, Functions, and Graphs

Constructed Functions

Functions, Limits, and Continuity

Linear Functions and Models Project

Tuition Fees Project

United States Population

Ingredients of Change: Nonlinear Models

Exponential Functions and Models

Logarithmic Functions and Models

Logistic Functions and Models

Polynomial Functions and Models

Choosing a Function to Fit Data Project

Compulsory School Laws Project

Fund-Raising Campaign

Describing Change: Rates

Change, Percentage Change, and Average Rates of Change

Instantaneous Rates of Change

Derivatives

Numerically Finding Slopes

Algebraically Finding Slopes Project

Fee-Refund Schedules Project

Doubling Time

Determining Change: Derivatives

Drawing Rate-of-Change Graphs

Simple Rate-of-Change Formulas

More Simple Rate-of-Change Formulas

The Chain Rule

The Product Rule Project

Superhighway Project

Fertility Rates

Analyzing Change: Applications of Derivatives

Approximating Change

Relative and Absolute Extreme Points

Inflection Points

Derivatives in Action

Interconnected Change: Related Rates Project

Hunting License Fees Project

Fund-Raising Campaign

Accumulating Change: Limits of Sums and the Definite Integral

Results of Change and Area Approximations

Limit of Sums, Accumulated Change, and the Definite Integral

Accumulation Functions

The Fundamental Theorem

The Definite Integral

Average Value and Average Rate of Change

Antiderivative Limitations Project

Acceleration, Velocity, and Distance Project

Estimating Growth

Analyzing Accumulated Change: Integrals in Action

Perpetual Accumulation and Improper Integrals

Streams in Business and Biology

Integrals in Economics

Probability Distributions and Density Functions Project

Arch Art

Repetitive Change: Cycles and Trigonometry

Functions of Angles: Sine and Cosine

Cyclic Functions as Models

Rates of Change and Derivatives

Extrema and Points of Inflection

Accumulation in Cycles Project

Seasonal Sales Project

Lake Tahoe Levels

Ingredients of Multivariable Change: Models, Graphs, Rates

Multivariable Functions and Contour Graphs

Cross-Sectional Models and Rates of Change

Partial Rates of Change

Compensating for Change Project

Competitive and Complementary Products Project

Expert Witness

Analyzing Multivariable Change: Optimization

Multivariable Critical Points

Multivariable Optimization

Optimization Under Constraints

Least-Squares Optimization Project

Snow Cover Project

Carbonated Beverage Packaging

Answers to Odd Activities

Index of Applications

Subject Index

Chapter 11 and the Appendices are available via the Internet

Dynamics of Change: Differential Equations and Proportionality

Differential Equations and Slope Fields

Separable Differential Equations

Numerically Estimating by Using Differential Equations: Euler's Method

Second-Order Differential Equations Chapter 11

Answers to Odd Activities

Trigonometry Basics Trigonometry Basics Answers to Appendix A

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

Skill Strengthening

Skill Strengthening

Skill Strengthening

Skill Strengthening

Skill Strengthening

Skill Strengthening

Answers to Appendix C

Solutions to Appendix C

Table of Contents provided by Publisher. All Rights Reserved.