Chapter 1 Functions and Graphs
1.1 Slope and Linear Functions
1.2 Polynomial Functions
1.3 Rational and Radical 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
Answers
Index
