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Calculus Concepts : An Informal Approach to the Mathematics of Change

Calculus Concepts : An Informal Approach to the Mathematics of Change - 2nd edition

ISBN13: 978-0618121755

Cover of Calculus Concepts : An Informal Approach to the Mathematics of Change 2ND 02 (ISBN 978-0618121755)
ISBN13: 978-0618121755
ISBN10: 0618121757
Cover type:
Edition/Copyright: 2ND 02
Publisher: Houghton Mifflin Harcourt
Published: 2002
International: No

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Calculus Concepts : An Informal Approach to the Mathematics of Change - 2ND 02 edition

ISBN13: 978-0618121755

Don Latorre, John Kenelly, Iris Fetta, Cynthia Harris and Carpenter

ISBN13: 978-0618121755
ISBN10: 0618121757
Cover type:
Edition/Copyright: 2ND 02
Publisher: Houghton Mifflin Harcourt

Published: 2002
International: No
Summary

Designed for the one- to two-semester Business/Applied Calculus course that commonly requires the use of graphing utilities and spreadsheets, Calculus Concepts takes an applications-based approach that involves modeling, the use and interpretation of real-world data, and the use of technology. The text helps build bridges between the mathematics of calculus and the real-world concepts students will face in their future careers. Students use real data and graphing technology to build their own models and interpret results.

The Second Edition has been revised to provide instructors with greater flexibility. New topics and levels of academic rigor have been incorporated to accommodate a variety of course needs, but may be omitted without loss of continuity. Instructors may simply choose the emphasis and topics most suited to their particular course.

  • New! Chapter Applications have been revised and updated to correspond to an activity in the chapter.
  • Concept Objectives present each chapter's goals in a chapter-opening list, divided into concepts and skills.
  • Concept Inventories at the end of each section summarize the key concepts and skills developed within that section.
  • Concept Check lists at the end of each chapter summarize the main concepts and skills taught in the chapter.
  • Concept Review/Chapter Tests at the end of each chapter provide more practice with techniques and concepts. Answers to these tests are included in the answer key at the back of the text.
  • New! Integrated web resources in the Second Edition feature special web icons in the text margin that refer students to additional pedagogical support available on the text-specific web site, including self-tests, algebraic tutorials, additional practice problems, data updates, a glossary, and more.
  • This edition features hundreds of updated models and data sets as well as many new activities.
  • New! Technology Guides for Excel and Graphing Calculators show students how to solve certain examples in the text using their particular technology. The manuals include instructions for the TI-83, TI-86, and TI-89 calculators as well as for Excel. Sections of the manuals are referenced in the text by a technology icon.

Author Bio

LaTorre, Don : Clemson University


Kenelly, John : Clemson University


Fetta, Iris : Clemson University


Cynthia Harris


Laurel Carpenter

Table of Contents

1. Ingredients of Change: Functions and Linear Models

1.1 Models, Functions, and Graphs
1.2 Functions: Discrete and Continuous
1.3 Constructed Functions
1.4 Limits: Describing Function Behavior
1.5 Linear Functions and Models
Project 1.1 Tuition Fees
Project 1.2 Finding Data

2. Ingredients of Change: Nonlinear Models

2.1 Exponential and Logarithmic Functions and Models
2.2 Exponential Models in Action
2.3 Logistic Functions and Models
2.4 Polynomial Functions and Models
2.5 Shifting Data
2.6 Choosing a Model
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 Drawing Rate-of-Change Graphs
Project 3.1 Fee-Refund Schedules
Project 3.2 Doubling Time

4. Determining Change: Derivatives

4.1 Numerically Finding Slopes
4.2 Algebraically Finding Slopes
4.3 Simple Rate-of-Change Formulas
4.4 More Simple Rate-of Change Formulas
4.5 The Chain Rule
4.6 The Product Rule
Project 4.1 Fertility Rates
Project 4.2 Superhighway

5. Analyzing Change: Applications of Derivatives

5.1 Approximating Change
5.2 Relative and Absolute Extreme Points
5.3 Derivatives in Action
5.4 Inflection Points
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 Area Approximations
6.2 The Definite Integral as a Limit of Sums
6.3 Accumulation Functions
6.4 The Fundamental Theorem
6.5 The Definite Integral
6.6 Additional Definite Integral Topics
Project 6.1 Acceleration, Velocity, and Distance
Project 6.2 Estimating Growth

7. Analyzing Accumulated Change: Integrals in Action

7.1 Differences of Accumulated Changes
7.2 Streams in Business and Biology
7.3 Integrals in Economics
7.4 Average Value and Average Rate of Change
7.5 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 Cross-Sectional Models and Multivariable Functions
9.2 Contour Graphs
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

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

11. Dynamics of Change: Related Rates, Differential Equations, and Proportionality

11.1 Differential Equations and Slope Fields
11.2 Separable Differential Equations
11.3 Numerically Estimating Using Differential Equations; Euler's Method
11.4 Second-Order Differential Equations

Answers to Selected Activities
Subject Index

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