# Calculus for the Life Sciences

Published Date: Oct 18, 2005

Chapter 1    Functions and Graphs

1.1    Slope and Linear Functions

1.2    Polynomial Functions

1.4    Trigonometric Functions

1.5    Trigonometric Functions and the Unit Circle

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Carbon Dioxide Concentrations

Chapter 2    Differentiation

2.1    Limits and Continuity:  Numerically and Graphically

2.2    Limits: Algebraically

2.3    Average Rates of Change

2.4    Differentiation Using Limits of Difference Quotients

2.5    Differentiation Techniques: Introduction

2.6    Instantaneous Rates of Change

2.7    Differentiation Techniques:  The Product and Quotient Rules

2.8    The Chain Rule

2.9    Higher-Order Derivatives

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Rate of Epidemic Spread: SARS

Chapter 3    Applications of Differentiation

3.1    Using the First Derivatives to Find Maximum and Minimum Values and Sketch Graphs

3.2    Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs

3.3    Graph Sketching:  Asymptotes and Rational Functions

3.4    Using Derivatives to Find Absolute Maximum and Minimum Values

3.5    Maximum-Minimum Problems

3.6    Approximation Techniques

3.7    Implicit Differentiation of Related Rates

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Polymorphism

Chapter 4    Exponential and Logarithmic Functions

4.1    Exponential Functions

4.2    Logarithmic Functions

4.3    Applications:  The Uninhibited Growth Model, dP/dt = kP

4.4    Applications:  Decay

4.5    The Derivatives of ax and logax

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Maximum Sustainable Harvest

Chapter 5    Integration

5.1    Integration

5.2    Riemann Sums and Definite Integrals

5.3    Fundamental Theorem of Calculus

5.4    Properties of Definite Integrals

5.5    Integration Techniques: Substitution

5.6    Integration Techniques:  Integration by Parts

5.7    Integration Techniques:  Tables and Technology

5.8    Volume

5.9    Improper Integrals

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Estimating Dinosaur Mass

Chapter 6    Matrices

6.1    Matrix Operations

6.2    Solving Linear Systems of Equations

6.3    Finding a Matrix Inverse and Determinant

6.4    Computing Eigenvalues and Eigenvectors

6.5    Solving Difference Equations

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Population Growth

Chapter 7    Functions of Several Variables

7.1    Functions of Several Variables

7.2    Partial Derivatives

7.3    Maximum-Minimum Problems

7.4    An Application:  The Method of Least Squares

7.5    Multiple Integration

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Stocking Fish

Chapter 8    First-Order Differential Equations

8.1    Differential Equations and Initial-Value Problems

8.2    Linear First-Order Differential Equations

8.3    Stability of Autonomous Differential Equations

8.4    Separable Differential Equations

8.5    Numerical Solutions of Differential Equations

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Larvae and Forest Defoliation

Chapter 9    Higher-Order and Systems of Differential Equations

9.1    Higher-Order Homogeneous Differential Equations

9.2    Higher-Order Nonhomogeneous Differential Equations

9.3    Systems of Linear Differential Equations

9.4    Matrices and Trajectories

9.5    Models of Population Biology

9.6    Numerical Methods

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Epidemics

Chapter 10    Probability

10.1    Probability

10.2    Multiplication Trees and Bayes’ Rule

10.3    The Binomial Distribution

10.4    Expected Value and Standard Deviation for Discrete Random Variables

10.5    Continuous Random Variables

10.6    Poisson Process

10.7    The Normal Distribution

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION:  Axenic Cultures

Appendix A:    Review of Basic Algebra

Appendix B:    Functions

Tables

Integration Formulas

Areas for a Standard Normal Distribution

Index

Package ISBN-13: 9780321481238

Includes this title packaged with:

• Student Solutions Manual for Calculus for the Life Sciences
Marvin L. Bittinger, Neal Brand, John Quintanilla

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