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by Geoffrey C. Berresford and Andrew M. Rockett

Edition: 99Copyright: 1999

Publisher: Houghton Mifflin Harcourt

Published: 1999

International: No

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Berresford's lively approach to calculus, now available for a one- or two-term course in applied calculus and finite mathematics, is designed to enrich learning for students majoring in business, economics, life sciences, and social sciences. The text's engaging approach shows students how to use calculus to predict the national debt, to study global warming, to maximize longevity, to analyze trends in the AIDS epidemic, to estimate the dangers of cigarette smoking, and in countless other relevant applications. A wealth of exercise sets providing numerous additional applications helps demonstrate for students that calculus is more than merely manipulating abstract symbols, but rather is deeply connected to everyday life.

- The text provides more graphing calculator examples and exercises than any other book; these may be omitted without loss of continuity, making use of a graphing calculator an optional tool for exploration.
- Numerous applications of high interest to students cover a wide range of subjects, from sports to genetic engineering, spread of disease, gambling, personal wealth, and environmental issues, to name a few.
- Unique to Berresford's texts, interactive "Practice Problems" with full solutions are offered after more difficult worked-out examples to provide students with extra practice and immediate feedback on their understanding of complex concepts.
- Seven to ten extensive writing and/or collaborative exercises conclude each chapter.
- Margin annotations restate much of the mathematics in words and provide explanations for the steps of a solution.
- End-of-section summaries, in addition to more comprehensive end-of-chapter summaries, help students retain concepts as they progress through the text.
- Instructors may select applications at a glance from the Application Index at the front of the text.

*Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions, Review Exercises, and Projects and Essays.*

**0. Functions**

Real Numbers, Inequalities and Lines

Exponents

Functions

Functions, Continued

Exponential Functions

Logarithmic Functions

__I. Finite Mathematics__

**1. Mathematics of Finance**

Simple Interest

Compound Interest

Annuities

Amortization

**2. Matrices and Systems of Equations**

Systems of Two Linear Equations in Two Variables

Matrices and Linear Equations in Two Variables

Matrix Row Reduction and Systems of Linear Equations

Matrix Arithmetic

Inverse Matrices and Systems of Linear Equations

Three Applications

**3. Linear Programming**

Linear Inequalities

Two-Variable Linear Programming Problems

The Simplex Method for Standard Maximum Problems

Duality and Standard Minimum Problems

Non-Standard Problems

**4. Probability**

Counting Techniques

Probability Spaces

Conditional Probability and Independence

Random Variables and Distributions

**5. Statistics**

Random Samples and Data Organization

Measures of Central Tendency

Measures of Variations

Normal Distributions

__II. Calculus__

**6. Derivatives and Their Uses**

Limits and Continuity

Slopes, Rates of Change, and Derivatives

Some Differentiation Formulas

The Product and Quotient Rules

Higher-Order Derivatives

The Chain Rule and the Generalized Power Rule

Nondifferentiable Functions

**7. Further Applications of Derivatives**

Graphing Using the First Derivative

Graphing Using the First and Second Derivatives

Optimization

Further Applications of Optimization

Optimizing Lot Size and Harvest Size

Implicit Differentiation and Related Rates

**8. Exponential and Logarithmic Functions**

Review of Exponential and Logarithmic Functions

Differentiation of Exponential and Logarithmic Functions

Two Applications to Economics: Related Rates and Elasticity of Demand

**9. Integration and Its Applications**

Antiderivatives

Integration Using Logarithmic and Exponential Functions

Definite Integrals and Areas

Further Applications of Definite Integrals: Average Value and Area Between Curves

Two Applications to Economics: Consumers' Surplus and Income Distribution

Integration by Substitution

**10. Integration Techniques and Differential Equations**

Integration by Parts

Integration Using Tables

Improper Integrals

Numerical Integration

Differential Equations

Further Applications of Differential Equations: Three Models of Growth

**11. Calculus of Several Variables**

Functions of Several Variables

Partial Derivatives

Optimizing Functions of Several Variables

Least Squares

LaGrange Multipliers and Constrained Optimization

Total Differentials and Approximate Changes

Multiple Integrals

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Summary

Berresford's lively approach to calculus, now available for a one- or two-term course in applied calculus and finite mathematics, is designed to enrich learning for students majoring in business, economics, life sciences, and social sciences. The text's engaging approach shows students how to use calculus to predict the national debt, to study global warming, to maximize longevity, to analyze trends in the AIDS epidemic, to estimate the dangers of cigarette smoking, and in countless other relevant applications. A wealth of exercise sets providing numerous additional applications helps demonstrate for students that calculus is more than merely manipulating abstract symbols, but rather is deeply connected to everyday life.

- The text provides more graphing calculator examples and exercises than any other book; these may be omitted without loss of continuity, making use of a graphing calculator an optional tool for exploration.
- Numerous applications of high interest to students cover a wide range of subjects, from sports to genetic engineering, spread of disease, gambling, personal wealth, and environmental issues, to name a few.
- Unique to Berresford's texts, interactive "Practice Problems" with full solutions are offered after more difficult worked-out examples to provide students with extra practice and immediate feedback on their understanding of complex concepts.
- Seven to ten extensive writing and/or collaborative exercises conclude each chapter.
- Margin annotations restate much of the mathematics in words and provide explanations for the steps of a solution.
- End-of-section summaries, in addition to more comprehensive end-of-chapter summaries, help students retain concepts as they progress through the text.
- Instructors may select applications at a glance from the Application Index at the front of the text.

Table of Contents

*Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions, Review Exercises, and Projects and Essays.*

**0. Functions**

Real Numbers, Inequalities and Lines

Exponents

Functions

Functions, Continued

Exponential Functions

Logarithmic Functions

__I. Finite Mathematics__

**1. Mathematics of Finance**

Simple Interest

Compound Interest

Annuities

Amortization

**2. Matrices and Systems of Equations**

Systems of Two Linear Equations in Two Variables

Matrices and Linear Equations in Two Variables

Matrix Row Reduction and Systems of Linear Equations

Matrix Arithmetic

Inverse Matrices and Systems of Linear Equations

Three Applications

**3. Linear Programming**

Linear Inequalities

Two-Variable Linear Programming Problems

The Simplex Method for Standard Maximum Problems

Duality and Standard Minimum Problems

Non-Standard Problems

**4. Probability**

Counting Techniques

Probability Spaces

Conditional Probability and Independence

Random Variables and Distributions

**5. Statistics**

Random Samples and Data Organization

Measures of Central Tendency

Measures of Variations

Normal Distributions

__II. Calculus__

**6. Derivatives and Their Uses**

Limits and Continuity

Slopes, Rates of Change, and Derivatives

Some Differentiation Formulas

The Product and Quotient Rules

Higher-Order Derivatives

The Chain Rule and the Generalized Power Rule

Nondifferentiable Functions

**7. Further Applications of Derivatives**

Graphing Using the First Derivative

Graphing Using the First and Second Derivatives

Optimization

Further Applications of Optimization

Optimizing Lot Size and Harvest Size

Implicit Differentiation and Related Rates

**8. Exponential and Logarithmic Functions**

Review of Exponential and Logarithmic Functions

Differentiation of Exponential and Logarithmic Functions

Two Applications to Economics: Related Rates and Elasticity of Demand

**9. Integration and Its Applications**

Antiderivatives

Integration Using Logarithmic and Exponential Functions

Definite Integrals and Areas

Further Applications of Definite Integrals: Average Value and Area Between Curves

Two Applications to Economics: Consumers' Surplus and Income Distribution

Integration by Substitution

**10. Integration Techniques and Differential Equations**

Integration by Parts

Integration Using Tables

Improper Integrals

Numerical Integration

Differential Equations

Further Applications of Differential Equations: Three Models of Growth

**11. Calculus of Several Variables**

Functions of Several Variables

Partial Derivatives

Optimizing Functions of Several Variables

Least Squares

LaGrange Multipliers and Constrained Optimization

Total Differentials and Approximate Changes

Multiple Integrals

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 1999

International: No

Published: 1999

International: No

Berresford's lively approach to calculus, now available for a one- or two-term course in applied calculus and finite mathematics, is designed to enrich learning for students majoring in business, economics, life sciences, and social sciences. The text's engaging approach shows students how to use calculus to predict the national debt, to study global warming, to maximize longevity, to analyze trends in the AIDS epidemic, to estimate the dangers of cigarette smoking, and in countless other relevant applications. A wealth of exercise sets providing numerous additional applications helps demonstrate for students that calculus is more than merely manipulating abstract symbols, but rather is deeply connected to everyday life.

- The text provides more graphing calculator examples and exercises than any other book; these may be omitted without loss of continuity, making use of a graphing calculator an optional tool for exploration.
- Numerous applications of high interest to students cover a wide range of subjects, from sports to genetic engineering, spread of disease, gambling, personal wealth, and environmental issues, to name a few.
- Unique to Berresford's texts, interactive "Practice Problems" with full solutions are offered after more difficult worked-out examples to provide students with extra practice and immediate feedback on their understanding of complex concepts.
- Seven to ten extensive writing and/or collaborative exercises conclude each chapter.
- Margin annotations restate much of the mathematics in words and provide explanations for the steps of a solution.
- End-of-section summaries, in addition to more comprehensive end-of-chapter summaries, help students retain concepts as they progress through the text.
- Instructors may select applications at a glance from the Application Index at the front of the text.

*Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions, Review Exercises, and Projects and Essays.*

**0. Functions**

Real Numbers, Inequalities and Lines

Exponents

Functions

Functions, Continued

Exponential Functions

Logarithmic Functions

__I. Finite Mathematics__

**1. Mathematics of Finance**

Simple Interest

Compound Interest

Annuities

Amortization

**2. Matrices and Systems of Equations**

Systems of Two Linear Equations in Two Variables

Matrices and Linear Equations in Two Variables

Matrix Row Reduction and Systems of Linear Equations

Matrix Arithmetic

Inverse Matrices and Systems of Linear Equations

Three Applications

**3. Linear Programming**

Linear Inequalities

Two-Variable Linear Programming Problems

The Simplex Method for Standard Maximum Problems

Duality and Standard Minimum Problems

Non-Standard Problems

**4. Probability**

Counting Techniques

Probability Spaces

Conditional Probability and Independence

Random Variables and Distributions

**5. Statistics**

Random Samples and Data Organization

Measures of Central Tendency

Measures of Variations

Normal Distributions

__II. Calculus__

**6. Derivatives and Their Uses**

Limits and Continuity

Slopes, Rates of Change, and Derivatives

Some Differentiation Formulas

The Product and Quotient Rules

Higher-Order Derivatives

The Chain Rule and the Generalized Power Rule

Nondifferentiable Functions

**7. Further Applications of Derivatives**

Graphing Using the First Derivative

Graphing Using the First and Second Derivatives

Optimization

Further Applications of Optimization

Optimizing Lot Size and Harvest Size

Implicit Differentiation and Related Rates

**8. Exponential and Logarithmic Functions**

Review of Exponential and Logarithmic Functions

Differentiation of Exponential and Logarithmic Functions

Two Applications to Economics: Related Rates and Elasticity of Demand

**9. Integration and Its Applications**

Antiderivatives

Integration Using Logarithmic and Exponential Functions

Definite Integrals and Areas

Further Applications of Definite Integrals: Average Value and Area Between Curves

Two Applications to Economics: Consumers' Surplus and Income Distribution

Integration by Substitution

**10. Integration Techniques and Differential Equations**

Integration by Parts

Integration Using Tables

Improper Integrals

Numerical Integration

Differential Equations

Further Applications of Differential Equations: Three Models of Growth

**11. Calculus of Several Variables**

Functions of Several Variables

Partial Derivatives

Optimizing Functions of Several Variables

Least Squares

LaGrange Multipliers and Constrained Optimization

Total Differentials and Approximate Changes

Multiple Integrals