# Calculus with Applications, 12th edition

• Margaret L. Lial,
• Raymond N. Greenwell,
• Nathan P. Ritchey

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## Overview

Calculus with Applications, 13th Edition prepares you for career success with timely applications throughout. Known for using real data in their examples and exercises, the authors make mathematics meaningful and relevant in the narrative, examples, exercise sets and supplementary resources. You'll have ample opportunity to relate what you're learning to career situations through the Apply It question at the beginning of sections, the applied examples and exercises, and the Extended Application at the end of each chapter.

ISBN-13: 9780137419340

Subject: Finite Math & Applied Calculus

Category: Applied Calculus

## Overview

Preface

Prerequisite Skills Diagnostic Test

R. Algebra Reference

R.1 Polynomials

R.2 Factoring

R.3 Rational Expressions

R.4 Equations

R.5 Inequalities

R.6 Exponents

1. Linear Functions

1.1 Slopes and Equations of Lines

1.2 Linear Functions and Applications

1.3 The Least Squares Line

Chapter 1 Review

Extended Application: Predicting Life Expectancy

2. Nonlinear Functions

2.1 Properties of Functions

2.2 Quadratic Functions; Translation and Reflection

2.3 Polynomial and Rational Functions

2.4 Exponential Functions

2.5 Logarithmic Functions

2.6 Applications: Growth and Decay; Mathematics of Finance

Chapter 2 Review

Extended Application: Power Functions

3. The Derivative

3.1 Limits

3.2 Continuity

3.3 Rates of Change

3.4 Definition of the Derivative

3.5 Graphical Differentiation

Chapter 3 Review

Extended Application: A Model for Drugs Administered Intravenously

4. Calculating the Derivative

4.1 Techniques for Finding Derivatives

4.2 Derivatives of Products and Quotients

4.3 The Chain Rule

4.4 Derivatives of Exponential Functions

4.5 Derivatives of Logarithmic Functions

Chapter 4 Review

Extended Application: Electric Potential and Electric Field

5. Graphs and the Derivative

5.1 Increasing and Decreasing Functions

5.2 Relative Extrema

5.3 Higher Derivatives, Concavity, and the Second Derivative Test

5.4 Curve Sketching

Chapter 5 Review

Extended Application: A Drug Concentration Model for Orally Administered Medications

6. Applications of the Derivative

6.1 Absolute Extrema

6.2 Applications of Extrema

6.4 Implicit Differentiation

6.5 Related Rates

6.6 Differentials: Linear Approximation

Chapter 6 Review

Extended Application: A Total Model for a Training Program

7. Integration

7.1 Antiderivatives

7.2 Substitution

7.3 Area and the Definite Integral

7.4 The Fundamental Theorem of Calculus

7.5 The Area Between Two Curves

7.6 Numerical Integration

Chapter 7 Review

Extended Application Estimating Depletion Dates for Minerals

8. Further Techniques and Applications of Integration

8.1 Integration by Parts

8.2 Volume and Average Value

8.3 Continuous Money Flow

8.4 Improper Integrals

Chapter 8 Review

Extended Application: Estimating Learning Curves in Manufacturing With Integrals

9. Multivariable Calculus

9.1 Functions of Several Variables

9.2 Partial Derivatives

9.3 Maxima and Minima

9.4 Lagrange Multipliers

9.5 Total Differentials and Approximations

9.6 Double Integrals

Chapter 9 Review

Extended Application: Using Multivariable Fitting to Create a Response Surface Design

10. Differential Equations

10.1 Solutions of Elementary and Separable Differential Equations

10.2 Linear First-Order Differential Equations

10.3 Euler's Method

10.4 Applications of Differential Equations

Chapter 10 Review

Extended Application: Pollution of the Great Lakes

11. Probability and Calculus

11.1 Continuous Probability Models

11.2 Expected Value and Variance of Continuous Random Variables

11.3 Special Probability Density Functions

Chapter 11 Review

Extended Application Exponential Waiting Times

12. Sequences and Series

12.1 Geometric Sequences

12.2 Annuities: An Application of Sequences

12.3 Taylor Polynomials at 0

12.4 Infinite Series

12.5 Taylor Series at 0

12.6 Newton's Method

12.7 L'Hôpital's Rule

Chapter 12 Review

Extended Application: Living Assistance and Subsidized Housing

13. The Trigonometric Functions

13.1 Definitions of the Trigonometric Functions

13.2 Derivatives of Trigonometric Functions

13.3 Integrals of Trigonometric Functions

Chapter 13 Review

Extended Application: The Shortest Time and the Cheapest Path

Appendix

1. Solutions to Prerequisite Skills Diagnostic Test
2. Tables

Credits

Index of Applications

Index

Sources

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