## Description

**Calculus for the Life Sciences**features interesting, relevant applications that motivate students and highlight the utility of mathematics for the life sciences. This edition also features new ways to engage students with the material, such as Your Turn exercises.

**Note: **You are purchasing a standalone product; MyMathLab does not come packaged with this content. MyMathLab is not a self-paced technology and should only be purchased when required by an instructor. If you would like to purchase *both *the physical text and MyMathLab, search for:

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0321964039 / 9780321964038 Calculus for the Life Sciences

## Table of Contents

**R. Algebra Reference**

R.1 Polynomials

R.2 Factoring

R.3 Rational Expressions

R.4 Equations

R.5 Inequalities

R.6 Exponents

R.7 Radicals

**1. Functions**

1.1 Lines and Linear Functions

1.2 The Least Squares Line

1.3 Properties of Functions

1.4 Quadratic Functions; Translation and Reflection

1.5 Polynomial and Rational Functions

Chapter Review

Extended Application: Using Extrapolation to Predict Life Expectancy

**2. Exponential, Logarithmic, and Trigonometric Functions**

2.1 Exponential Functions

2.2 Logarithmic Functions

2.3 Applications: Growth and Decay

2.4 Trigonometric Functions

Chapter 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 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

4.6 Derivatives of Trigonometric Functions

Chapter Review

Extended Application: Managing Renewable Resources

**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 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

6.3 Implicit Differentiation

6.4 Related Rates

6.5 Differentials: Linear Approximation

Chapter Review

Extended Application: A Total Cost 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

Chapter Review

Extended Application: Estimating Depletion Dates for Minerals

**8. Further Techniques and Applications of Integration**

8.1 Numerical Integration

8.2 Integration by Parts

8.3 Volume and Average Value

8.4 Improper Integrals

Chapter Review

Extended Application: Flow Systems

**9. Multivariable Calculus**

9.1 Functions of Several Variables

9.2 Partial Derivatives

9.3 Maxima and Minima

9.4 Total Differentials and Approximations

9.5 Double Integrals

Chapter Review

Extended Application: Optimization for a Predator

**10. Matrices**

10.1 Solution of Linear Systems

10.2 Addition and Subtraction of Matrices

10.3 Multiplication of Matrices

10.4 Matrix Inverses

10.5 Eigenvalues and Eigenvectors

Chapter Review

Extended Application: Contagion

**11. Differential Equations**

11.1 Solutions of Elementary and Separable Differential Equations

11.2 Linear First-Order Differential Equations

11.3 Euler's Method

11.4 Linear Systems of Differential Equations

11.5 Non-Linear Systems of Differential Equations

11.6 Applications of Differential Equations

Chapter Review

Extended Application: Pollution of the Great Lakes

**12. Probability**

12.1 Sets

12.2 Introduction to Probability

12.3 Conditional Probability; Independent Events; Bayes' Theorem

12.4 Discrete Random Variables; Applications to Decision Making

Chapter Review

Extended Application: Medical Diagnosis

**13. Probability and Calculus**

13.1 Continuous Probability Models

13.2 Expected Value and Variance of Continuous Random Variables.

13.3 Special Probability Density Functions

Chapter Review

Extended Application: Exponential Waiting Times

**14. Discrete Dynamical Systems**

14.1 Sequences

14.2 Equilibrium Points

14.3 Determining Stability

Chapter Review

Extended Application: Mathematical Modeling in a Dynamic World

**Special Topics (available online)**

**Sequences and Series**

Geometric Sequences

Annuities: An Application of Sequences

Taylor Polynomials

Infinite Series

Taylor Series

Newton’s Method

L’Hôpital’s Rule

**Markov Chains**

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

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