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by Larry J. Goldstein, David I. Lay, David I. Schneider and Nakhle Asmar

Cover type: HardbackEdition: 11TH 07

Copyright: 2007

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

Larry J. Goldstein, David I. Lay, David I. Schneider and Nakhle Asmar

Cover type: HardbackEdition: 11TH 07

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This text is geared towards a one semester course in applied calculus.

This extremely readable, highly regarded, and widely adopted text presents innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formula--pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises--has proven to be tremendously successful with both students and instructors.

**Features**

- Exercise sets:
- Carefully designed, building in level of difficulty so that instructors can chose those exercises appropriate for their students.
- Thoroughly tested and very diverse.
- Technology exercises offered at the ends of each section.

- Applications: Contain up-to-date and realistic data to illustrate to students the relevance of these concepts.
- Examples: Contains many more worked examples than is customary, many of which include real data.
- Practice Problems: Each section concludes with ~5 problems that focus on concepts that are potentially confusion. Complete solutions are provided.
- ''Warnings!'' which provide tips on common pitfalls and mistakes appear at relevant times.
- Extensive TI Calculator help: Easy-to-understand instructions for using calculators are provided in 4 appendices

Preface

Introduction

**0 Functions**

0.1 Functions and Their Graphs

0.2 Some Important Functions

0.3 The Algebra of Functions

0.4 Zeros of Functions--The Quadratic Formula and Factoring

0.5 Exponents and Power Functions

0.6 Functions and Graphs in Applications

**1 The Derivative**

1.1 The Slope of a Straight Line

1.2 The Slope of a Curve at a Point

1.3 The Derivative

1.4 Limits and the Derivative

1.5 Differentiability and Continuity

1.6 Some Rules for Differentiation

1.7 More About Derivatives

1.8 The Derivative as a Rate of Change

**2 Applications of the Derivative**

2.1 Describing Graphs of Functions

2.2 The First and Second Derivative Rules

2.3 The First and Second Derivative Tests and Curve Sketching

2.4 Curve Sketching (Conclusion)

2.5 Optimization Problems

2.6 Further Optimization Problems

2.7 Applications of Derivatives to Business and Economics

**3 Techniques of Differentiation**

3.1 The Product and Quotient Rules

3.2 The Chain Rule and the General Power Rule

3.3 Implicit Differentiation and Related Rates

**4 Logarithm Functions**

4.1 Exponential Functions

4.2 The Exponential Function ex

4.3 Differentiation of Exponential Functions

4.4 The Natural Logarithm Function

4.5 The Derivative of ln x

4.6 Properties of the Natural Logarithm Function

**5 Applications of the Exponential and**

Natural Logarithm Functions

5.1 Exponential Growth and Decay

5.2 Compound Interest

5.3 Applications of the Natural Logarithm Function to Economics

5.4 Further Exponential Models

**6 The Definite Integral**

6.1 Antidifferentiation

6.2 Areas and Riemann Sums

6.3 Definite Integrals and the Fundamental Theorem

6.4 Areas in the xy-Plane

6.5 Applications of the Definite Integral

**7 Functions of Several Variables**

7.1 Examples of Functions of Several Variables

7.2 Partial Derivatives

7.3 Maxima and Minima of Functions of Several Variables

7.4 Lagrange Multipliers and Constrained Optimization

7.5 The Method of Least Squares

7.6 Double Integrals

**8 The Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Sine and the Cosine

8.3 Differentiation and Integration of sin t and cos t

8.4 The Tangent and Other Trigonometric Functions

**9 Techniques of Integration**

9.1 Integration by Substitution

9.2 Integration by Parts

9.3 Evaluation of Definite Integrals

9.4 Approximation of Definite Integrals

9.5 Some Applications of the Integral

9.6 Improper Integrals

**10 Differential Equations**

10.1 Solutions of Differential Equations

10.2 Separation of Variables

10.3 First-Order Linear Differential Equations

10.4 Applications of First-Order Linear Differential Equations

10.5 Graphing Solutions of Differential Equations

10.6 Applications of Differential Equations

10.7 Numerical Solution of Differential Equations

**11 Taylor Polynomials and Infinite Series**

11.1 Taylor Polynomials

11.2 The Newton-Raphson Algorithm

11.3 Infinite Series

11.4 Series with Positive Terms

11.5 Taylor Series

**12 Probability and Calculus**

12.1 Discrete Random Variables

12.2 Continuous Random Variables

12.3 Expected Value and Variance

12.4 Exponential and Normal Random Variables

12.5 Poisson and Geometric Random Variables

Appendix A Calculus and the TI-82 Calculator

Appendix B Calculus and the TI-83/TI-83 Plus/TI-84 Plus Calculators

Appendix C Calculus and the TI-85 Calculator

Appendix D Calculus and the TI-86 Calculator

Appendix E Areas under the Standard Normal Curve

Answers to Exercises

Index I1

Summary

This text is geared towards a one semester course in applied calculus.

This extremely readable, highly regarded, and widely adopted text presents innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formula--pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises--has proven to be tremendously successful with both students and instructors.

**Features**

- Exercise sets:
- Carefully designed, building in level of difficulty so that instructors can chose those exercises appropriate for their students.
- Thoroughly tested and very diverse.
- Technology exercises offered at the ends of each section.

- Applications: Contain up-to-date and realistic data to illustrate to students the relevance of these concepts.
- Examples: Contains many more worked examples than is customary, many of which include real data.
- Practice Problems: Each section concludes with ~5 problems that focus on concepts that are potentially confusion. Complete solutions are provided.
- ''Warnings!'' which provide tips on common pitfalls and mistakes appear at relevant times.
- Extensive TI Calculator help: Easy-to-understand instructions for using calculators are provided in 4 appendices

Table of Contents

Preface

Introduction

**0 Functions**

0.1 Functions and Their Graphs

0.2 Some Important Functions

0.3 The Algebra of Functions

0.4 Zeros of Functions--The Quadratic Formula and Factoring

0.5 Exponents and Power Functions

0.6 Functions and Graphs in Applications

**1 The Derivative**

1.1 The Slope of a Straight Line

1.2 The Slope of a Curve at a Point

1.3 The Derivative

1.4 Limits and the Derivative

1.5 Differentiability and Continuity

1.6 Some Rules for Differentiation

1.7 More About Derivatives

1.8 The Derivative as a Rate of Change

**2 Applications of the Derivative**

2.1 Describing Graphs of Functions

2.2 The First and Second Derivative Rules

2.3 The First and Second Derivative Tests and Curve Sketching

2.4 Curve Sketching (Conclusion)

2.5 Optimization Problems

2.6 Further Optimization Problems

2.7 Applications of Derivatives to Business and Economics

**3 Techniques of Differentiation**

3.1 The Product and Quotient Rules

3.2 The Chain Rule and the General Power Rule

3.3 Implicit Differentiation and Related Rates

**4 Logarithm Functions**

4.1 Exponential Functions

4.2 The Exponential Function ex

4.3 Differentiation of Exponential Functions

4.4 The Natural Logarithm Function

4.5 The Derivative of ln x

4.6 Properties of the Natural Logarithm Function

**5 Applications of the Exponential and**

Natural Logarithm Functions

5.1 Exponential Growth and Decay

5.2 Compound Interest

5.3 Applications of the Natural Logarithm Function to Economics

5.4 Further Exponential Models

**6 The Definite Integral**

6.1 Antidifferentiation

6.2 Areas and Riemann Sums

6.3 Definite Integrals and the Fundamental Theorem

6.4 Areas in the xy-Plane

6.5 Applications of the Definite Integral

**7 Functions of Several Variables**

7.1 Examples of Functions of Several Variables

7.2 Partial Derivatives

7.3 Maxima and Minima of Functions of Several Variables

7.4 Lagrange Multipliers and Constrained Optimization

7.5 The Method of Least Squares

7.6 Double Integrals

**8 The Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Sine and the Cosine

8.3 Differentiation and Integration of sin t and cos t

8.4 The Tangent and Other Trigonometric Functions

**9 Techniques of Integration**

9.1 Integration by Substitution

9.2 Integration by Parts

9.3 Evaluation of Definite Integrals

9.4 Approximation of Definite Integrals

9.5 Some Applications of the Integral

9.6 Improper Integrals

**10 Differential Equations**

10.1 Solutions of Differential Equations

10.2 Separation of Variables

10.3 First-Order Linear Differential Equations

10.4 Applications of First-Order Linear Differential Equations

10.5 Graphing Solutions of Differential Equations

10.6 Applications of Differential Equations

10.7 Numerical Solution of Differential Equations

**11 Taylor Polynomials and Infinite Series**

11.1 Taylor Polynomials

11.2 The Newton-Raphson Algorithm

11.3 Infinite Series

11.4 Series with Positive Terms

11.5 Taylor Series

**12 Probability and Calculus**

12.1 Discrete Random Variables

12.2 Continuous Random Variables

12.3 Expected Value and Variance

12.4 Exponential and Normal Random Variables

12.5 Poisson and Geometric Random Variables

Appendix A Calculus and the TI-82 Calculator

Appendix B Calculus and the TI-83/TI-83 Plus/TI-84 Plus Calculators

Appendix C Calculus and the TI-85 Calculator

Appendix D Calculus and the TI-86 Calculator

Appendix E Areas under the Standard Normal Curve

Answers to Exercises

Index I1

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2007

International: No

Published: 2007

International: No

This text is geared towards a one semester course in applied calculus.

This extremely readable, highly regarded, and widely adopted text presents innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formula--pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises--has proven to be tremendously successful with both students and instructors.

**Features**

- Exercise sets:
- Carefully designed, building in level of difficulty so that instructors can chose those exercises appropriate for their students.
- Thoroughly tested and very diverse.
- Technology exercises offered at the ends of each section.

- Applications: Contain up-to-date and realistic data to illustrate to students the relevance of these concepts.
- Examples: Contains many more worked examples than is customary, many of which include real data.
- Practice Problems: Each section concludes with ~5 problems that focus on concepts that are potentially confusion. Complete solutions are provided.
- ''Warnings!'' which provide tips on common pitfalls and mistakes appear at relevant times.
- Extensive TI Calculator help: Easy-to-understand instructions for using calculators are provided in 4 appendices

Preface

Introduction

**0 Functions**

0.1 Functions and Their Graphs

0.2 Some Important Functions

0.3 The Algebra of Functions

0.4 Zeros of Functions--The Quadratic Formula and Factoring

0.5 Exponents and Power Functions

0.6 Functions and Graphs in Applications

**1 The Derivative**

1.1 The Slope of a Straight Line

1.2 The Slope of a Curve at a Point

1.3 The Derivative

1.4 Limits and the Derivative

1.5 Differentiability and Continuity

1.6 Some Rules for Differentiation

1.7 More About Derivatives

1.8 The Derivative as a Rate of Change

**2 Applications of the Derivative**

2.1 Describing Graphs of Functions

2.2 The First and Second Derivative Rules

2.3 The First and Second Derivative Tests and Curve Sketching

2.4 Curve Sketching (Conclusion)

2.5 Optimization Problems

2.6 Further Optimization Problems

2.7 Applications of Derivatives to Business and Economics

**3 Techniques of Differentiation**

3.1 The Product and Quotient Rules

3.2 The Chain Rule and the General Power Rule

3.3 Implicit Differentiation and Related Rates

**4 Logarithm Functions**

4.1 Exponential Functions

4.2 The Exponential Function ex

4.3 Differentiation of Exponential Functions

4.4 The Natural Logarithm Function

4.5 The Derivative of ln x

4.6 Properties of the Natural Logarithm Function

**5 Applications of the Exponential and**

Natural Logarithm Functions

5.1 Exponential Growth and Decay

5.2 Compound Interest

5.3 Applications of the Natural Logarithm Function to Economics

5.4 Further Exponential Models

**6 The Definite Integral**

6.1 Antidifferentiation

6.2 Areas and Riemann Sums

6.3 Definite Integrals and the Fundamental Theorem

6.4 Areas in the xy-Plane

6.5 Applications of the Definite Integral

**7 Functions of Several Variables**

7.1 Examples of Functions of Several Variables

7.2 Partial Derivatives

7.3 Maxima and Minima of Functions of Several Variables

7.4 Lagrange Multipliers and Constrained Optimization

7.5 The Method of Least Squares

7.6 Double Integrals

**8 The Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Sine and the Cosine

8.3 Differentiation and Integration of sin t and cos t

8.4 The Tangent and Other Trigonometric Functions

**9 Techniques of Integration**

9.1 Integration by Substitution

9.2 Integration by Parts

9.3 Evaluation of Definite Integrals

9.4 Approximation of Definite Integrals

9.5 Some Applications of the Integral

9.6 Improper Integrals

**10 Differential Equations**

10.1 Solutions of Differential Equations

10.2 Separation of Variables

10.3 First-Order Linear Differential Equations

10.4 Applications of First-Order Linear Differential Equations

10.5 Graphing Solutions of Differential Equations

10.6 Applications of Differential Equations

10.7 Numerical Solution of Differential Equations

**11 Taylor Polynomials and Infinite Series**

11.1 Taylor Polynomials

11.2 The Newton-Raphson Algorithm

11.3 Infinite Series

11.4 Series with Positive Terms

11.5 Taylor Series

**12 Probability and Calculus**

12.1 Discrete Random Variables

12.2 Continuous Random Variables

12.3 Expected Value and Variance

12.4 Exponential and Normal Random Variables

12.5 Poisson and Geometric Random Variables

Appendix A Calculus and the TI-82 Calculator

Appendix B Calculus and the TI-83/TI-83 Plus/TI-84 Plus Calculators

Appendix C Calculus and the TI-85 Calculator

Appendix D Calculus and the TI-86 Calculator

Appendix E Areas under the Standard Normal Curve

Answers to Exercises

Index I1