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by Raymond A. Barnett, Michael R. Ziegler and Karl E. Byleen

Edition: 10TH 05Copyright: 2005

Publisher: Prentice Hall, Inc.

Published: 2005

International: No

Raymond A. Barnett, Michael R. Ziegler and Karl E. Byleen

Edition: 10TH 05
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For a one-semester or one-quarter course covering calculus for students majoring in business, economics, social sciences, or life sciences.

This mid-level text covers calculus with an emphasis on cross-discipline principles and practices. Student-friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.

**PART ONE. A LIBRARY OF ELEMENTARY FUNCTIONS. CHAPTER 1. A Beginning Library of Elementary Functions. **

1-1 Functions.

1-2 Elementary Functions: Graphs and Transformations.

1-3 Linear Functions and Straight Lines.

1-4 Quadratic Functions.

Group Activity 1: Introduction to Regression Analysis.

Group Activity 2: Mathematical Modeling in Business.

**CHAPTER 2. Additional Elementary Functions. **

2-1 Polynomial and Rational Functions.

2-2 Exponential Functions.

2-3 Logarithmic Functions.

Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions.

Group Activity 2: Comparing Regression Models.

**PART TWO. CALCULUS. CHAPTER 3. The Derivative. **

3-1 Introduction to Limits.

3-2 Limits and Continuity.

3-3 The Derivative.

3-4 Derivative of Constants, Power Forms, and Sums.

3-5 Derivatives of Products and Quotients.

3-6 Chain Rule: Power Form.

3-7 Marginal Analysis in Business and Economics.

Group Activity 1: Minimal Average Cost.

Group Activity 2: Numerical Differentiation on a Graphing Utility.

**CHAPTER 4. Graphing and Optimization. **

4-1 First Derivative and Graphs.

4-2 Second Derivative and Graphs.

4-3 Curve Sketching Techniques; Unified and Extended.

4-4 Optimization; Absolute Maxima and Minima.

Group Activity 1: Maximizing Profit.

Group Activity 2: Minimizing Construction Costs.

**CHAPTER 5. Additional Derivative Topics**

5-1 The Constant e and Continuous Compound Interest.

5-2 Derivatives of Logarithmic and Exponential Functions.

5-3 Chain Rule: General Form.

5-4 Implicit Differentiation.

5-5 Related Rates.

Group Activity 1: Elasticity of Demand.

Group Activity 2: Point of Diminishing Returns.

**CHAPTER 6. Integration. **

6-1 Antiderivatives and Indefinite Integrals.

6-2 Integration by Substitution.

6-3 Differential Equations; Growth and Decay.

6-4 The Definite Integral.

6-5 The Fundamental Theorem of Calculus.

Group Activity 1: Simpson's Rule.

Group Activity 2: Bell-Shaped Curves.

**CHAPTER 7. Additional Integration Topics. **

7-1 Area Between Curves.

7-2 Applications in Business and Economics.

7-3 Integration by Parts.

7-4 Integration Using Tables.

Group Activity 1: Analysis of Income Concentration from Raw Data.

Group Activity 2: Grain Exchange.

**CHAPTER 8. Multivariable Calculus. **

8-1 Functions of Several Variables.

8-2 Partial Derivatives.

8-3 Maxima and Minima.

8-4 Maxima and Minima Using Lagrange Multipliers.

8-5 Method of Least Squares.

8-6 Double Integrals Over Rectangular Regions.

Group Activity 1: City Planning.

Group Activity 2: Numerical Integration of Multivariable Functions.

**CHAPTER 9. Trigonometric Functions. **

9-1 Trigonometric Functions Review.

9-2 Derivatives of Trigonometric Functions.

9-3 Integrations of Trigonometric Functions.

Group Activity 1: Seasonal Business Cycles.

Group Activity 2: Heating Degree Days.

Summary

For a one-semester or one-quarter course covering calculus for students majoring in business, economics, social sciences, or life sciences.

This mid-level text covers calculus with an emphasis on cross-discipline principles and practices. Student-friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.

Table of Contents

**PART ONE. A LIBRARY OF ELEMENTARY FUNCTIONS. CHAPTER 1. A Beginning Library of Elementary Functions. **

1-1 Functions.

1-2 Elementary Functions: Graphs and Transformations.

1-3 Linear Functions and Straight Lines.

1-4 Quadratic Functions.

Group Activity 1: Introduction to Regression Analysis.

Group Activity 2: Mathematical Modeling in Business.

**CHAPTER 2. Additional Elementary Functions. **

2-1 Polynomial and Rational Functions.

2-2 Exponential Functions.

2-3 Logarithmic Functions.

Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions.

Group Activity 2: Comparing Regression Models.

**PART TWO. CALCULUS. CHAPTER 3. The Derivative. **

3-1 Introduction to Limits.

3-2 Limits and Continuity.

3-3 The Derivative.

3-4 Derivative of Constants, Power Forms, and Sums.

3-5 Derivatives of Products and Quotients.

3-6 Chain Rule: Power Form.

3-7 Marginal Analysis in Business and Economics.

Group Activity 1: Minimal Average Cost.

Group Activity 2: Numerical Differentiation on a Graphing Utility.

**CHAPTER 4. Graphing and Optimization. **

4-1 First Derivative and Graphs.

4-2 Second Derivative and Graphs.

4-3 Curve Sketching Techniques; Unified and Extended.

4-4 Optimization; Absolute Maxima and Minima.

Group Activity 1: Maximizing Profit.

Group Activity 2: Minimizing Construction Costs.

**CHAPTER 5. Additional Derivative Topics**

5-1 The Constant e and Continuous Compound Interest.

5-2 Derivatives of Logarithmic and Exponential Functions.

5-3 Chain Rule: General Form.

5-4 Implicit Differentiation.

5-5 Related Rates.

Group Activity 1: Elasticity of Demand.

Group Activity 2: Point of Diminishing Returns.

**CHAPTER 6. Integration. **

6-1 Antiderivatives and Indefinite Integrals.

6-2 Integration by Substitution.

6-3 Differential Equations; Growth and Decay.

6-4 The Definite Integral.

6-5 The Fundamental Theorem of Calculus.

Group Activity 1: Simpson's Rule.

Group Activity 2: Bell-Shaped Curves.

**CHAPTER 7. Additional Integration Topics. **

7-1 Area Between Curves.

7-2 Applications in Business and Economics.

7-3 Integration by Parts.

7-4 Integration Using Tables.

Group Activity 1: Analysis of Income Concentration from Raw Data.

Group Activity 2: Grain Exchange.

**CHAPTER 8. Multivariable Calculus. **

8-1 Functions of Several Variables.

8-2 Partial Derivatives.

8-3 Maxima and Minima.

8-4 Maxima and Minima Using Lagrange Multipliers.

8-5 Method of Least Squares.

8-6 Double Integrals Over Rectangular Regions.

Group Activity 1: City Planning.

Group Activity 2: Numerical Integration of Multivariable Functions.

**CHAPTER 9. Trigonometric Functions. **

9-1 Trigonometric Functions Review.

9-2 Derivatives of Trigonometric Functions.

9-3 Integrations of Trigonometric Functions.

Group Activity 1: Seasonal Business Cycles.

Group Activity 2: Heating Degree Days.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2005

International: No

Published: 2005

International: No

This mid-level text covers calculus with an emphasis on cross-discipline principles and practices. Student-friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.

**PART ONE. A LIBRARY OF ELEMENTARY FUNCTIONS. CHAPTER 1. A Beginning Library of Elementary Functions. **

1-1 Functions.

1-2 Elementary Functions: Graphs and Transformations.

1-3 Linear Functions and Straight Lines.

1-4 Quadratic Functions.

Group Activity 1: Introduction to Regression Analysis.

Group Activity 2: Mathematical Modeling in Business.

**CHAPTER 2. Additional Elementary Functions. **

2-1 Polynomial and Rational Functions.

2-2 Exponential Functions.

2-3 Logarithmic Functions.

Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions.

Group Activity 2: Comparing Regression Models.

**PART TWO. CALCULUS. CHAPTER 3. The Derivative. **

3-1 Introduction to Limits.

3-2 Limits and Continuity.

3-3 The Derivative.

3-4 Derivative of Constants, Power Forms, and Sums.

3-5 Derivatives of Products and Quotients.

3-6 Chain Rule: Power Form.

3-7 Marginal Analysis in Business and Economics.

Group Activity 1: Minimal Average Cost.

Group Activity 2: Numerical Differentiation on a Graphing Utility.

**CHAPTER 4. Graphing and Optimization. **

4-1 First Derivative and Graphs.

4-2 Second Derivative and Graphs.

4-3 Curve Sketching Techniques; Unified and Extended.

4-4 Optimization; Absolute Maxima and Minima.

Group Activity 1: Maximizing Profit.

Group Activity 2: Minimizing Construction Costs.

**CHAPTER 5. Additional Derivative Topics**

5-1 The Constant e and Continuous Compound Interest.

5-2 Derivatives of Logarithmic and Exponential Functions.

5-3 Chain Rule: General Form.

5-4 Implicit Differentiation.

5-5 Related Rates.

Group Activity 1: Elasticity of Demand.

Group Activity 2: Point of Diminishing Returns.

**CHAPTER 6. Integration. **

6-1 Antiderivatives and Indefinite Integrals.

6-2 Integration by Substitution.

6-3 Differential Equations; Growth and Decay.

6-4 The Definite Integral.

6-5 The Fundamental Theorem of Calculus.

Group Activity 1: Simpson's Rule.

Group Activity 2: Bell-Shaped Curves.

**CHAPTER 7. Additional Integration Topics. **

7-1 Area Between Curves.

7-2 Applications in Business and Economics.

7-3 Integration by Parts.

7-4 Integration Using Tables.

Group Activity 1: Analysis of Income Concentration from Raw Data.

Group Activity 2: Grain Exchange.

**CHAPTER 8. Multivariable Calculus. **

8-1 Functions of Several Variables.

8-2 Partial Derivatives.

8-3 Maxima and Minima.

8-4 Maxima and Minima Using Lagrange Multipliers.

8-5 Method of Least Squares.

8-6 Double Integrals Over Rectangular Regions.

Group Activity 1: City Planning.

Group Activity 2: Numerical Integration of Multivariable Functions.

**CHAPTER 9. Trigonometric Functions. **

9-1 Trigonometric Functions Review.

9-2 Derivatives of Trigonometric Functions.

9-3 Integrations of Trigonometric Functions.

Group Activity 1: Seasonal Business Cycles.

Group Activity 2: Heating Degree Days.