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by Larry J. Goldstein, David C. Lay and David I. Schneider

Edition: 8TH 99Copyright: 1999

Publisher: Prentice Hall, Inc.

Published: 1999

International: No

Larry J. Goldstein, David C. Lay and David I. Schneider

Edition: 8TH 99
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Once again, these extremely readable, highly regarded, and widely adopted texts present 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. What would the benefit to your students be of using a text which blends practical applications with mathematical concepts?

**Features**

- NEW - Details the ways in which technology can be used to foster understanding of several topics while it facilitates computation.
- NEW - Ends each chapter with a Review of Fundamental Concepts, helping students focus on the chapter's key points.
- NEW - Places greater emphasis on the significance of differential equations in applications involving exponential functions.
- NEW - Customized calculus software is available through the study guide.
- NEW - Companion website supports and extends the materials presented in the text.
- NEW - All graphs of functions have been redrawn using Mathematicia.
- Reinforces class lessons with carefully designed exercise sets, and challenges students to make their own connections.
- Minimizes prerequisites, allowing those who have forgotten much of their high school mathematics to start anew with this self-contained material.

* (NOTE: Calculus and Its Applications, 8 edition consists of Chapters 0-12. Brief Calculus and Its Applications, 8 edition consists of Chapters 0-8.) *

**Preface Introduction **

Functions and Their Graphs.

Some Important Functions.

The Algebra of Functions.

Zeros of Functions.

The Quadratic Formula and Factoring.

Exponents and Power Functions.

Functions and Graphs in Applications.

**1. The Derivative**

The Slope of a Straight Line.

The Slope of a Curve at a Point.

The Derivative.

Limits and the Derivative.

Differentiability and Continuity.

Some Rules for Differentiation.

More About Derivatives.

The Derivative as a Rate of Change.

**2. Applications of the Derivative **

Describing Graphs of Functions.

The First and Second Derivative Rules.

Curve Sketching (Introduction.) Curve Sketching (Conclusion.) Optimization Problems.

Further Optimization Problems.

Applications of Calculus to Business and Economics.

**3. Techniques of Differentiation**

The Product and Quotient Rules.

The Chain Rule and the General Power Rule.

Implicit Differentiation and Related Rates.

**4. The Exponential and Natural Logarithm Functions **

Exponential Functions.

The Exponential Function.

Differentiation of Exponential Functions.

The Natural Logarithm Function.

The Derivative of ln x.

Properties of the Natural Logarithm Function.

**5. Applications of the Exponential and Natural Logarithm Functions**

Exponential Growth and Decay.

Compound Interest.

Applications of the Natural Logarithm Function to Economics.

Further Exponential Models.

**6. The Definite Integral **

Antidifferentiation.

Areas and Reimann Sums.

Definite Integrals and the Fundamental Theorem.

Areas in the xy-Plane.

Applications of the Definite Integral.

**7. Functions of Several Variables**

Examples of Functions of Several Variables.

Partial Derivatives.

Maxima and Minima of Functions of Several Variables.

Lagrange Multipliers and Constrained Optimization.

The Method of Least Squares.

Double Integrals.

**8. The Trigonometric Functions **

Radian Measure of Angles.

The Sine and the Cosine.

Differentiation of sin t and cos t.

The Tangent and Other Trigonometric Functions.

**9. Techniques of Integration **

Integration by Substitution.

Integration by Parts.

Evaluation of Definite Integrals.

Approximation of Definite Integrals.

Some Applications of the Integral.

Improper Integrals.

**10. Differential Equations**

Solutions of Differential Equations.

Separation of Variables.

Numerical Solution of Differential Equations.

Qualitative Theory of Differential Equations.

Applications of Differential Equations.

**11. Taylor Polynomials and Infinite Series **

Taylor Polynomials.

The Newton-Raphson Algorithm.

Infinite Series.

Series with Positive Terms.

Taylor Series.

**12. Probability and Calculus**

Discrete Random Variables.

Continuous Random Variables.

Expected Value and Variance.

Exponential and Normal Random Variables.

Poisson and Geometric Random Variables.

*Appendices *

Appendix A. Calculus and the TI-82 Calculator.

Appendix B. Calculus and the TI-83 Calculator.

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.

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Summary

Once again, these extremely readable, highly regarded, and widely adopted texts present 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. What would the benefit to your students be of using a text which blends practical applications with mathematical concepts?

**Features**

- NEW - Details the ways in which technology can be used to foster understanding of several topics while it facilitates computation.
- NEW - Ends each chapter with a Review of Fundamental Concepts, helping students focus on the chapter's key points.
- NEW - Places greater emphasis on the significance of differential equations in applications involving exponential functions.
- NEW - Customized calculus software is available through the study guide.
- NEW - Companion website supports and extends the materials presented in the text.
- NEW - All graphs of functions have been redrawn using Mathematicia.
- Reinforces class lessons with carefully designed exercise sets, and challenges students to make their own connections.
- Minimizes prerequisites, allowing those who have forgotten much of their high school mathematics to start anew with this self-contained material.

Table of Contents

* (NOTE: Calculus and Its Applications, 8 edition consists of Chapters 0-12. Brief Calculus and Its Applications, 8 edition consists of Chapters 0-8.) *

**Preface Introduction **

Functions and Their Graphs.

Some Important Functions.

The Algebra of Functions.

Zeros of Functions.

The Quadratic Formula and Factoring.

Exponents and Power Functions.

Functions and Graphs in Applications.

**1. The Derivative**

The Slope of a Straight Line.

The Slope of a Curve at a Point.

The Derivative.

Limits and the Derivative.

Differentiability and Continuity.

Some Rules for Differentiation.

More About Derivatives.

The Derivative as a Rate of Change.

**2. Applications of the Derivative **

Describing Graphs of Functions.

The First and Second Derivative Rules.

Curve Sketching (Introduction.) Curve Sketching (Conclusion.) Optimization Problems.

Further Optimization Problems.

Applications of Calculus to Business and Economics.

**3. Techniques of Differentiation**

The Product and Quotient Rules.

The Chain Rule and the General Power Rule.

Implicit Differentiation and Related Rates.

**4. The Exponential and Natural Logarithm Functions **

Exponential Functions.

The Exponential Function.

Differentiation of Exponential Functions.

The Natural Logarithm Function.

The Derivative of ln x.

Properties of the Natural Logarithm Function.

**5. Applications of the Exponential and Natural Logarithm Functions**

Exponential Growth and Decay.

Compound Interest.

Applications of the Natural Logarithm Function to Economics.

Further Exponential Models.

**6. The Definite Integral **

Antidifferentiation.

Areas and Reimann Sums.

Definite Integrals and the Fundamental Theorem.

Areas in the xy-Plane.

Applications of the Definite Integral.

**7. Functions of Several Variables**

Examples of Functions of Several Variables.

Partial Derivatives.

Maxima and Minima of Functions of Several Variables.

Lagrange Multipliers and Constrained Optimization.

The Method of Least Squares.

Double Integrals.

**8. The Trigonometric Functions **

Radian Measure of Angles.

The Sine and the Cosine.

Differentiation of sin t and cos t.

The Tangent and Other Trigonometric Functions.

**9. Techniques of Integration **

Integration by Substitution.

Integration by Parts.

Evaluation of Definite Integrals.

Approximation of Definite Integrals.

Some Applications of the Integral.

Improper Integrals.

**10. Differential Equations**

Solutions of Differential Equations.

Separation of Variables.

Numerical Solution of Differential Equations.

Qualitative Theory of Differential Equations.

Applications of Differential Equations.

**11. Taylor Polynomials and Infinite Series **

Taylor Polynomials.

The Newton-Raphson Algorithm.

Infinite Series.

Series with Positive Terms.

Taylor Series.

**12. Probability and Calculus**

Discrete Random Variables.

Continuous Random Variables.

Expected Value and Variance.

Exponential and Normal Random Variables.

Poisson and Geometric Random Variables.

*Appendices *

Appendix A. Calculus and the TI-82 Calculator.

Appendix B. Calculus and the TI-83 Calculator.

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.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 1999

International: No

Published: 1999

International: No

Once again, these extremely readable, highly regarded, and widely adopted texts present 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. What would the benefit to your students be of using a text which blends practical applications with mathematical concepts?

**Features**

- NEW - Details the ways in which technology can be used to foster understanding of several topics while it facilitates computation.
- NEW - Ends each chapter with a Review of Fundamental Concepts, helping students focus on the chapter's key points.
- NEW - Places greater emphasis on the significance of differential equations in applications involving exponential functions.
- NEW - Customized calculus software is available through the study guide.
- NEW - Companion website supports and extends the materials presented in the text.
- NEW - All graphs of functions have been redrawn using Mathematicia.
- Reinforces class lessons with carefully designed exercise sets, and challenges students to make their own connections.
- Minimizes prerequisites, allowing those who have forgotten much of their high school mathematics to start anew with this self-contained material.

* (NOTE: Calculus and Its Applications, 8 edition consists of Chapters 0-12. Brief Calculus and Its Applications, 8 edition consists of Chapters 0-8.) *

**Preface Introduction **

Functions and Their Graphs.

Some Important Functions.

The Algebra of Functions.

Zeros of Functions.

The Quadratic Formula and Factoring.

Exponents and Power Functions.

Functions and Graphs in Applications.

**1. The Derivative**

The Slope of a Straight Line.

The Slope of a Curve at a Point.

The Derivative.

Limits and the Derivative.

Differentiability and Continuity.

Some Rules for Differentiation.

More About Derivatives.

The Derivative as a Rate of Change.

**2. Applications of the Derivative **

Describing Graphs of Functions.

The First and Second Derivative Rules.

Curve Sketching (Introduction.) Curve Sketching (Conclusion.) Optimization Problems.

Further Optimization Problems.

Applications of Calculus to Business and Economics.

**3. Techniques of Differentiation**

The Product and Quotient Rules.

The Chain Rule and the General Power Rule.

Implicit Differentiation and Related Rates.

**4. The Exponential and Natural Logarithm Functions **

Exponential Functions.

The Exponential Function.

Differentiation of Exponential Functions.

The Natural Logarithm Function.

The Derivative of ln x.

Properties of the Natural Logarithm Function.

**5. Applications of the Exponential and Natural Logarithm Functions**

Exponential Growth and Decay.

Compound Interest.

Applications of the Natural Logarithm Function to Economics.

Further Exponential Models.

**6. The Definite Integral **

Antidifferentiation.

Areas and Reimann Sums.

Definite Integrals and the Fundamental Theorem.

Areas in the xy-Plane.

Applications of the Definite Integral.

**7. Functions of Several Variables**

Examples of Functions of Several Variables.

Partial Derivatives.

Maxima and Minima of Functions of Several Variables.

Lagrange Multipliers and Constrained Optimization.

The Method of Least Squares.

Double Integrals.

**8. The Trigonometric Functions **

Radian Measure of Angles.

The Sine and the Cosine.

Differentiation of sin t and cos t.

The Tangent and Other Trigonometric Functions.

**9. Techniques of Integration **

Integration by Substitution.

Integration by Parts.

Evaluation of Definite Integrals.

Approximation of Definite Integrals.

Some Applications of the Integral.

Improper Integrals.

**10. Differential Equations**

Solutions of Differential Equations.

Separation of Variables.

Numerical Solution of Differential Equations.

Qualitative Theory of Differential Equations.

Applications of Differential Equations.

**11. Taylor Polynomials and Infinite Series **

Taylor Polynomials.

The Newton-Raphson Algorithm.

Infinite Series.

Series with Positive Terms.

Taylor Series.

**12. Probability and Calculus**

Discrete Random Variables.

Continuous Random Variables.

Expected Value and Variance.

Exponential and Normal Random Variables.

Poisson and Geometric Random Variables.

*Appendices *

Appendix A. Calculus and the TI-82 Calculator.

Appendix B. Calculus and the TI-83 Calculator.

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.