Calculus for the Life Sciences

Calculus for the Life Sciences

• 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