# Calculus & Its Applications, 13th Edition

Published Date: Jan 30, 2013

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## Description

Calculus and Its Applications, Thirteenth Edition is a comprehensive, yet flexible, text for students majoring in business, economics, life science, or social sciences. The authors delve into greater mathematical depth than other texts while motivating students through relevant, up-to-date, applications drawn from students’ major fields of study. The authors motivate key ideas geometrically and intuitively, providing a solid foundation for the more abstract treatments that follow. Every chapter includes a large quantity of exceptional exercises—a hallmark of this text--that address skills, applications, concepts, and technology. The Thirteenth Edition includes updated applications, exercises, and technology coverage. The authors have also added more study tools, including a prerequisite skills diagnostic test and a greatly improved end-of-chapter summary, and made content improvements based on user reviews.

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

1.8 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 Section 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. The Exponential and Natural 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 The Definite Integral and Net Change of a Function

6.3 The Definite Integral and Area Under a Graph

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

8.2 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: Areas under the Standard Normal Curve

Index

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Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

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• MathXL -- Valuepack Access Card (12-month access), 2nd Edition
. . Pearson Education
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Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

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