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Calculus Concepts: An Informal Approach to the Mathematics of Change

By Donald R. LaTorre, John W. Kenelly, Iris B. Reed, Laurel R. Carpenter, Cynthia R. Harris, Sherry Biggers

5th Edition © 2012
Discipline:Mathematics
Course:Finite Mathematics / Applied Calculus
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Designed for a one or two-semester Applied Calculus course, this innovative text features a graphing calculator approach, incorporating real-life applications and such technology as graphing utilities and Excel® spreadsheets to help students learn mathematical skills that they will use in their lives and careers. The texts overall goal is to improve learning of basic calculus concepts by involving students with new material in a way that is different from traditional practice. The development of conceptual understanding coupled with a commitment to make calculus meaningful to the student are guiding forces. The material involves many applications of real situations through its data-driven, technology-based modeling approach. The ability to correctly interpret the mathematics of real-life situations is considered of equal importance to the understanding of the concepts of calculus.
CALCULUS CONCEPTS, Fifth Edition, presents concepts in a variety of forms, including algebraic, graphical, numeric, and verbal. Targeted toward students majoring in liberal arts, economics, business, management, and the life and social sciences, the text's focus on technology along with its use of real data and situations make it a sound choice to help students develop an intuitive, practical understanding of concepts.

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About this product

Designed for a one or two-semester Applied Calculus course, this innovative text features a graphing calculator approach, incorporating real-life applications and such technology as graphing utilities and Excel® spreadsheets to help students learn mathematical skills that they will use in their lives and careers. The texts overall goal is to improve learning of basic calculus concepts by involving students with new material in a way that is different from traditional practice. The development of conceptual understanding coupled with a commitment to make calculus meaningful to the student are guiding forces. The material involves many applications of real situations through its data-driven, technology-based modeling approach. The ability to correctly interpret the mathematics of real-life situations is considered of equal importance to the understanding of the concepts of calculus.
CALCULUS CONCEPTS, Fifth Edition, presents concepts in a variety of forms, including algebraic, graphical, numeric, and verbal. Targeted toward students majoring in liberal arts, economics, business, management, and the life and social sciences, the text's focus on technology along with its use of real data and situations make it a sound choice to help students develop an intuitive, practical understanding of concepts.

Abundant use of data underscores the data-driven nature of this book.

Each chapter opens with a real-life situation and several questions about the situation that can be answered using the concepts and skills to be covered.

Each section incorporates a brief concept development narrative, interspersed with Quick Examples that highlight specific skills as well as formal examples that illustrate the application of the skills and concepts in a real-world setting.

A NAVG (numeric, algebraic, verbal, and graphical) compass icon indicates places in the text where a concept is demonstrated through multiple representations. This feature helps students recognize connections between different representations, and is particularly helpful for students who use alternative learning styles.

Table of contents

Chapters

Cover
Title Page
Copyright Page
Contents
PREFACE
CHAPTER 1: Ingredients of Change: Functions and Limits
CHAPTER 2: Describing Change: Rates
CHAPTER 3: Determining Change: Derivatives
CHAPTER 4: Analyzing Change: Applications of Derivatives
CHAPTER 5: Accumulating Change: Limits of Sums and the Definite Integral
CHAPTER 6: Analyzing Accumulated Change: Integrals in Action
CHAPTER 7: Ingredients of Multivariable Change: Models, Graphs, Rates
CHAPTER 8: Analyzing Multivariable Change: Optimization
ANSWERS TO ODD ACTIVITIES
SUBJECT INDEX
Show more

CHAPTER 1: Ingredients of Change: Functions and Limits

1.1
Functions: Four Representations
Preview this section ↗
Representations of Change ↗
Functions ↗
Function Output from Different Perspectives ↗
Model Output and Units of Measure ↗
Function Input ↗
Is it a Function? ↗
Concept Inventory ↗
Activities ↗
1.2
Function Behavior and End Behavior Limits
A Function’s Behavior Described
Direction and Curvature
Limits and End Behavior
Concept Inventory
Activities
1.3
Limits and Continuity
Functions with Unbounded Output
Functions with Specific Limits
Where Left Meets Right
Where Is the Output Heading?
Continuous Functions
Limits–Algebraically
Concept Inventory
Activities
1.4
Linear Functions and Models
Representations of a Linear Function
Slope and Intercept
Slope and End Behavior of a Linear Function
Elements of a Model
Models from Perfectly Linear Data
Linear Models from Data
Interpretions of Slope
Data Alignment
Numerical Considerations in Reporting and Calculating Answers
Concept Inventory
Activities
1.5
Exponential Functions and Models
Representations of an Exponential Function
Constant Multiplier of an Exponential Function
Percentage Change
Exponential Models from Data
Doubling Time and Half-Life
Concept Inventory
Activities
1.6
Models in Finance
Time-Value of Money
Simple Interest
Compound Interest
Interest Rates—APR vs. APY
Frequent Conversion Periods
Concept Inventory
Activities
1.7
Constructed Functions
Constructed Functions in Business and Economics
Operations for Combining Functions
Function Composition
Inverse Functions
Composition of Inverse Functions
Inverse Functions—Algebraically
Concept Inventory
Activities
1.8
Logarithmic Functions and Models
Representations of a Logarithmic Function
Characteristic Behavior of Logarithmic Functions
Log Models from Data
Input-Data Alignment for a Log Models
The Exponential Model Connection
Concept Inventory
Activities
1.9
Quadratic Functions and Models
Representations of a Quadratic Function
Characteristic Behavior of Quadratic Functions
Quadratic Models from Data
Exponential, Log, or Quadratic?
Preliminary Steps in Choosing a Model
Concept Inventory
Activities
1.10
Logistic Functions and Models
Representations of a Logistic Function
Exponential Growth with Constraints
Logistic Models from Data
Concept Inventory
Activities
1.11
Cubic Functions and Models
Representations of a Cubic Model
Characteristic Behavior of Cubic Functions
Cubic Models from Data
Model Choices
Concept Inventory
Activities
1.12
Cyclic Functions and Models
Representations of a Sine Function
Characteristics of Sine Functions
Sine Models from Data
Concept Inventory
Activities
Chapter Summary
Concept Check
Review Activities
Show more

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