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by Stefan Waner

Edition: 3RD 04Copyright: 2004

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

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Stefan Waner and Steven Costenoble's APPLIED CALCULUS, Third Edition is designed to address the considerable challenge of generating enthusiasm and developing mathematical sophistication in applied mathematics courses offered on many college campuses. The new edition retains its engaging conversational style and focus on real data and real world applications of mathematics--a strategy that has proven to be pedagogically successful. The wealth of applications, the highly effective integrated, yet optional, use of graphing calculators or spreadsheets, and the robust supplemental Web site that has received praise from around the world, make Waner/Costenoble's text an outstanding choice.

**Benefits: **

- NEW! Chapter One has been revised to include expanded coverage of linear regression.
- NEW! The number of exercises has been increased by 17 percent with additional easier computational exercises at the start of many exercise sets and significantly more Communication and Reasoning exercises. Exercises and examples based on dated information have generally been replaced by more current versions.
- NEW! A new arrangement of exercise sets reflects increasing level of difficulty.
- NEW! A new four-color design calls out the many excellent pedagogical tools, making them more efficient tools for instructors and students.
- Unique integration of graphing calculators, spreadsheets (using Excel), and the Web, supports a wide range of instructional settings. The text is suitable for classes relying exclusively on graphing calculators, web-based technology, or Excel, a combination of these, or none of them.
- Clearly delineated and carefully structured discussions introduce many of the central concepts in three ways: numerically, graphically, and algebraically.
- Written in a conversational, student-oriented style, the text combines interactive pedagogical devices with solid mathematics and a flexible approach to technology, and effectively addresses the difficult issues of teaching less-than-enthusiastic students.
- A text-specific Web site rich in features offers interactive tutorials, review exercises, and online utilities for a variety of tasks like graphing, regression, and matrix algebra. The site enhances interest, learning, and comprehension.
- A large number of the examples and exercises use referenced real data from business, economics, the life sciences, and the social sciences, appropriately modified and streamlined to keep the applications tractable.
- A case study framework for chapter topics begins each chapter with a statement of an interesting problem that is revisited at the end of the chapter.
- NEW! The integrated discussions of Excel and graphing calculators as optional tools have been expanded.
- NEW! Trigonometric functions material has been placed in a separate chapter.
- NEW! An expanded treatment of limits includes an additional section on the concept of continuity. The discussion of the algebraic approach to limits is now in a section by itself.
- NEW! Chapter 2 has additional material on regression for all the non-linear functions, and this coverage has been added to the new Trigonometry chapter.
- NEW! A new (optional) section on logistic models and regression has been added to Chapter 2.
- NEW! The significantly revised Chapter 3 on derivatives consolidates the graphical and numerical approaches and includes more on the algebraic approach.
- NEW! The highly effective pedagogy from the second edition has been expanded with more "Quick Examples", more "Question and Answer Dialog" boxes, additional Excel and graphing calculator instructions, and additional Web site information.
- NEW! A new boxed-feature called "Guidelines" appears at the ends of sections to assist students in problem-solving.

**Waner, Stefan : Hofstra University **

Costenoble, Steven : Hofstra University

1. LINEAR FUNCTIONS AND MODELS

Introduction

Functions from the Numerical and Algebraic Viewpoints

Functions from the Graphical Viewpoint

Linear Functions

Linear Models

Linear Regression

Case Study: Modeling Spending on Internet Advertising

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions

2. NONLINEAR MODELS

Introduction

Quadratic Functions and Models

Exponential Functions and Models

Logarithmic Functions and Models

Logistic Functions and Models

Case Study: Checking up on Malthus

Optional Internet Topics: Inverse Functions

Linear and Exponential Regression

Using and Deriving Algebraic Properties of Logarithms

3. INTRODUCTION TO THE DERIVATIVE

Introduction

Average Rate of Change

The Derivative: Numerical and Graphical Viewpoints

The Derivative : Algebraic Viewpoint

Derivatives of Powers, Sums, and Constant Multiples

A First Application: Marginal Analysis

Limits: Numerical and Graphical Approaches

Limits and Continuity

Limits and Continuity: Algebraic Approach

Case Study: Reducing Sulfur Emissions

Optional Internet Topics: Sketching the Graph of the Derivative

Proof of the Power Rule

Continuity and Differentiability

4. TECHNIQUES OF DIFFERENTIATION

Introduction

The Product and Quotient Rules

The Chain Rule

Derivatives of Logarithmic and Exponential Functions

Implicit Differentiation

Case Study: Projecting Market Growth

Optional Internet Topic: Linear Approximation and Error Estimation

5. APPLICATIONS OF THE DERIVATIVE

Introduction

Maxima and Minima

Applications of Maxima and Minima

The Second Derivative and Analyzing Graphs

Related Rates

Elasticity

Case Study: Production Lot Size Management

6. THE INTEGRAL

Introduction

The Indefinite Integral

Substitution

The Definite Integral as a Sum: A Numerical Approach

The Definite Integral as Area: A Geometric Approach

The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus

Case Study: Wage Inflation

Optional Internet Topic: Numerical Integration

7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL

Introduction

Integration by Parts

Area Between Two Curves and Applications

Averages and Moving Averages

Continuous Income Streams

Improper Integrals and Applications

Differential Equations and Applications

Case Study: Estimating Tax Revenues

8. FUNCTIONS OF SEVERAL VARIABLES

Introduction

Functions of Several Variables from the Numerical and Algebraic Viewpoints

Three Dimensional Space and the Graph of a Function of Two Variables

Partial Derivatives

Maxima and Minima

Constrained Maxima and Minima and Applications

Double Integrals

Case Study: Modeling Household Income

9. TRIGONOMETRIC MODELS

Introduction

Trigonometric Functions, Models, and Regression

Derivatives of Trigonometric Functions and Applications

Integrals of Trigonometric Functions and Applications

Case Study: Predicting Cocoa Inventories

Appendix A: Algebra Review

Introduction

Real Numbers

Exponents and Radicals

Multiplying and Factoring Algebraic Equations

Rational Expressions

Solving Polynomial Equations

Solving Miscellaneous Equations

OPTIONAL INTERNET CHAPTERS

S

Calculus Applied to Probability and Statistics

Introduction

Continuous Random Variables and Histograms

Probability Density Functions: Uniform, Exponential, Normal, and Beta

Mean, Median, Variance and Standard Deviation

Case Study: Creating a Family Trust

Summary

Stefan Waner and Steven Costenoble's APPLIED CALCULUS, Third Edition is designed to address the considerable challenge of generating enthusiasm and developing mathematical sophistication in applied mathematics courses offered on many college campuses. The new edition retains its engaging conversational style and focus on real data and real world applications of mathematics--a strategy that has proven to be pedagogically successful. The wealth of applications, the highly effective integrated, yet optional, use of graphing calculators or spreadsheets, and the robust supplemental Web site that has received praise from around the world, make Waner/Costenoble's text an outstanding choice.

**Benefits: **

- NEW! Chapter One has been revised to include expanded coverage of linear regression.
- NEW! The number of exercises has been increased by 17 percent with additional easier computational exercises at the start of many exercise sets and significantly more Communication and Reasoning exercises. Exercises and examples based on dated information have generally been replaced by more current versions.
- NEW! A new arrangement of exercise sets reflects increasing level of difficulty.
- NEW! A new four-color design calls out the many excellent pedagogical tools, making them more efficient tools for instructors and students.
- Unique integration of graphing calculators, spreadsheets (using Excel), and the Web, supports a wide range of instructional settings. The text is suitable for classes relying exclusively on graphing calculators, web-based technology, or Excel, a combination of these, or none of them.
- Clearly delineated and carefully structured discussions introduce many of the central concepts in three ways: numerically, graphically, and algebraically.
- Written in a conversational, student-oriented style, the text combines interactive pedagogical devices with solid mathematics and a flexible approach to technology, and effectively addresses the difficult issues of teaching less-than-enthusiastic students.
- A text-specific Web site rich in features offers interactive tutorials, review exercises, and online utilities for a variety of tasks like graphing, regression, and matrix algebra. The site enhances interest, learning, and comprehension.
- A large number of the examples and exercises use referenced real data from business, economics, the life sciences, and the social sciences, appropriately modified and streamlined to keep the applications tractable.
- A case study framework for chapter topics begins each chapter with a statement of an interesting problem that is revisited at the end of the chapter.
- NEW! The integrated discussions of Excel and graphing calculators as optional tools have been expanded.
- NEW! Trigonometric functions material has been placed in a separate chapter.
- NEW! An expanded treatment of limits includes an additional section on the concept of continuity. The discussion of the algebraic approach to limits is now in a section by itself.
- NEW! Chapter 2 has additional material on regression for all the non-linear functions, and this coverage has been added to the new Trigonometry chapter.
- NEW! A new (optional) section on logistic models and regression has been added to Chapter 2.
- NEW! The significantly revised Chapter 3 on derivatives consolidates the graphical and numerical approaches and includes more on the algebraic approach.
- NEW! The highly effective pedagogy from the second edition has been expanded with more "Quick Examples", more "Question and Answer Dialog" boxes, additional Excel and graphing calculator instructions, and additional Web site information.
- NEW! A new boxed-feature called "Guidelines" appears at the ends of sections to assist students in problem-solving.

Author Bio

**Waner, Stefan : Hofstra University **

Costenoble, Steven : Hofstra University

Table of Contents

1. LINEAR FUNCTIONS AND MODELS

Introduction

Functions from the Numerical and Algebraic Viewpoints

Functions from the Graphical Viewpoint

Linear Functions

Linear Models

Linear Regression

Case Study: Modeling Spending on Internet Advertising

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions

2. NONLINEAR MODELS

Introduction

Quadratic Functions and Models

Exponential Functions and Models

Logarithmic Functions and Models

Logistic Functions and Models

Case Study: Checking up on Malthus

Optional Internet Topics: Inverse Functions

Linear and Exponential Regression

Using and Deriving Algebraic Properties of Logarithms

3. INTRODUCTION TO THE DERIVATIVE

Introduction

Average Rate of Change

The Derivative: Numerical and Graphical Viewpoints

The Derivative : Algebraic Viewpoint

Derivatives of Powers, Sums, and Constant Multiples

A First Application: Marginal Analysis

Limits: Numerical and Graphical Approaches

Limits and Continuity

Limits and Continuity: Algebraic Approach

Case Study: Reducing Sulfur Emissions

Optional Internet Topics: Sketching the Graph of the Derivative

Proof of the Power Rule

Continuity and Differentiability

4. TECHNIQUES OF DIFFERENTIATION

Introduction

The Product and Quotient Rules

The Chain Rule

Derivatives of Logarithmic and Exponential Functions

Implicit Differentiation

Case Study: Projecting Market Growth

Optional Internet Topic: Linear Approximation and Error Estimation

5. APPLICATIONS OF THE DERIVATIVE

Introduction

Maxima and Minima

Applications of Maxima and Minima

The Second Derivative and Analyzing Graphs

Related Rates

Elasticity

Case Study: Production Lot Size Management

6. THE INTEGRAL

Introduction

The Indefinite Integral

Substitution

The Definite Integral as a Sum: A Numerical Approach

The Definite Integral as Area: A Geometric Approach

The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus

Case Study: Wage Inflation

Optional Internet Topic: Numerical Integration

7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL

Introduction

Integration by Parts

Area Between Two Curves and Applications

Averages and Moving Averages

Continuous Income Streams

Improper Integrals and Applications

Differential Equations and Applications

Case Study: Estimating Tax Revenues

8. FUNCTIONS OF SEVERAL VARIABLES

Introduction

Functions of Several Variables from the Numerical and Algebraic Viewpoints

Three Dimensional Space and the Graph of a Function of Two Variables

Partial Derivatives

Maxima and Minima

Constrained Maxima and Minima and Applications

Double Integrals

Case Study: Modeling Household Income

9. TRIGONOMETRIC MODELS

Introduction

Trigonometric Functions, Models, and Regression

Derivatives of Trigonometric Functions and Applications

Integrals of Trigonometric Functions and Applications

Case Study: Predicting Cocoa Inventories

Appendix A: Algebra Review

Introduction

Real Numbers

Exponents and Radicals

Multiplying and Factoring Algebraic Equations

Rational Expressions

Solving Polynomial Equations

Solving Miscellaneous Equations

OPTIONAL INTERNET CHAPTERS

S

Calculus Applied to Probability and Statistics

Introduction

Continuous Random Variables and Histograms

Probability Density Functions: Uniform, Exponential, Normal, and Beta

Mean, Median, Variance and Standard Deviation

Case Study: Creating a Family Trust

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

Published: 2004

International: No

Stefan Waner and Steven Costenoble's APPLIED CALCULUS, Third Edition is designed to address the considerable challenge of generating enthusiasm and developing mathematical sophistication in applied mathematics courses offered on many college campuses. The new edition retains its engaging conversational style and focus on real data and real world applications of mathematics--a strategy that has proven to be pedagogically successful. The wealth of applications, the highly effective integrated, yet optional, use of graphing calculators or spreadsheets, and the robust supplemental Web site that has received praise from around the world, make Waner/Costenoble's text an outstanding choice.

**Benefits: **

- NEW! Chapter One has been revised to include expanded coverage of linear regression.
- NEW! The number of exercises has been increased by 17 percent with additional easier computational exercises at the start of many exercise sets and significantly more Communication and Reasoning exercises. Exercises and examples based on dated information have generally been replaced by more current versions.
- NEW! A new arrangement of exercise sets reflects increasing level of difficulty.
- NEW! A new four-color design calls out the many excellent pedagogical tools, making them more efficient tools for instructors and students.
- Unique integration of graphing calculators, spreadsheets (using Excel), and the Web, supports a wide range of instructional settings. The text is suitable for classes relying exclusively on graphing calculators, web-based technology, or Excel, a combination of these, or none of them.
- Clearly delineated and carefully structured discussions introduce many of the central concepts in three ways: numerically, graphically, and algebraically.
- Written in a conversational, student-oriented style, the text combines interactive pedagogical devices with solid mathematics and a flexible approach to technology, and effectively addresses the difficult issues of teaching less-than-enthusiastic students.
- A text-specific Web site rich in features offers interactive tutorials, review exercises, and online utilities for a variety of tasks like graphing, regression, and matrix algebra. The site enhances interest, learning, and comprehension.
- A large number of the examples and exercises use referenced real data from business, economics, the life sciences, and the social sciences, appropriately modified and streamlined to keep the applications tractable.
- A case study framework for chapter topics begins each chapter with a statement of an interesting problem that is revisited at the end of the chapter.
- NEW! The integrated discussions of Excel and graphing calculators as optional tools have been expanded.
- NEW! Trigonometric functions material has been placed in a separate chapter.
- NEW! An expanded treatment of limits includes an additional section on the concept of continuity. The discussion of the algebraic approach to limits is now in a section by itself.
- NEW! Chapter 2 has additional material on regression for all the non-linear functions, and this coverage has been added to the new Trigonometry chapter.
- NEW! A new (optional) section on logistic models and regression has been added to Chapter 2.
- NEW! The significantly revised Chapter 3 on derivatives consolidates the graphical and numerical approaches and includes more on the algebraic approach.
- NEW! The highly effective pedagogy from the second edition has been expanded with more "Quick Examples", more "Question and Answer Dialog" boxes, additional Excel and graphing calculator instructions, and additional Web site information.
- NEW! A new boxed-feature called "Guidelines" appears at the ends of sections to assist students in problem-solving.

**Waner, Stefan : Hofstra University **

Costenoble, Steven : Hofstra University

1. LINEAR FUNCTIONS AND MODELS

Introduction

Functions from the Numerical and Algebraic Viewpoints

Functions from the Graphical Viewpoint

Linear Functions

Linear Models

Linear Regression

Case Study: Modeling Spending on Internet Advertising

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions

2. NONLINEAR MODELS

Introduction

Quadratic Functions and Models

Exponential Functions and Models

Logarithmic Functions and Models

Logistic Functions and Models

Case Study: Checking up on Malthus

Optional Internet Topics: Inverse Functions

Linear and Exponential Regression

Using and Deriving Algebraic Properties of Logarithms

3. INTRODUCTION TO THE DERIVATIVE

Introduction

Average Rate of Change

The Derivative: Numerical and Graphical Viewpoints

The Derivative : Algebraic Viewpoint

Derivatives of Powers, Sums, and Constant Multiples

A First Application: Marginal Analysis

Limits: Numerical and Graphical Approaches

Limits and Continuity

Limits and Continuity: Algebraic Approach

Case Study: Reducing Sulfur Emissions

Optional Internet Topics: Sketching the Graph of the Derivative

Proof of the Power Rule

Continuity and Differentiability

4. TECHNIQUES OF DIFFERENTIATION

Introduction

The Product and Quotient Rules

The Chain Rule

Derivatives of Logarithmic and Exponential Functions

Implicit Differentiation

Case Study: Projecting Market Growth

Optional Internet Topic: Linear Approximation and Error Estimation

5. APPLICATIONS OF THE DERIVATIVE

Introduction

Maxima and Minima

Applications of Maxima and Minima

The Second Derivative and Analyzing Graphs

Related Rates

Elasticity

Case Study: Production Lot Size Management

6. THE INTEGRAL

Introduction

The Indefinite Integral

Substitution

The Definite Integral as a Sum: A Numerical Approach

The Definite Integral as Area: A Geometric Approach

The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus

Case Study: Wage Inflation

Optional Internet Topic: Numerical Integration

7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL

Introduction

Integration by Parts

Area Between Two Curves and Applications

Averages and Moving Averages

Continuous Income Streams

Improper Integrals and Applications

Differential Equations and Applications

Case Study: Estimating Tax Revenues

8. FUNCTIONS OF SEVERAL VARIABLES

Introduction

Functions of Several Variables from the Numerical and Algebraic Viewpoints

Three Dimensional Space and the Graph of a Function of Two Variables

Partial Derivatives

Maxima and Minima

Constrained Maxima and Minima and Applications

Double Integrals

Case Study: Modeling Household Income

9. TRIGONOMETRIC MODELS

Introduction

Trigonometric Functions, Models, and Regression

Derivatives of Trigonometric Functions and Applications

Integrals of Trigonometric Functions and Applications

Case Study: Predicting Cocoa Inventories

Appendix A: Algebra Review

Introduction

Real Numbers

Exponents and Radicals

Multiplying and Factoring Algebraic Equations

Rational Expressions

Solving Polynomial Equations

Solving Miscellaneous Equations

OPTIONAL INTERNET CHAPTERS

S

Calculus Applied to Probability and Statistics

Introduction

Continuous Random Variables and Histograms

Probability Density Functions: Uniform, Exponential, Normal, and Beta

Mean, Median, Variance and Standard Deviation

Case Study: Creating a Family Trust