Applied Calculus 5th Edition

Chapter Nine

MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS

Contents

9.1 Mathematical Modeling: Setting up a Differential Equation

Marine Harvesting

Net Worth of a Company

Pollution in a Lake

The Quantity of a Drug in the Body

The Logistic Model

9.2 Solutions of Differential Equations

Another Look at Marine Harvesting

Numerical Solutions

A Formula for the Solutions

Initial Conditions

General Solutions and Particular Solutions

9.3 Slope Fields

Existence and Uniqueness of Solutions

9.4 Exponential Growth and Decay

Population Growth

Continuously Compounded Interest

Pollution in the Great Lakes

The Quantity of a Drug in the Body

9.5 Applications and Modeling

The Quantity of a Drug in the Body

Solving dy/dt = k(y − A)

Equilibrium Solutions

Newton's Law of Heating and Cooling

9.6 Modeling the Interaction of Two Populations

A Predator-Prey Model: Robins and Worms

The Phase Plane

The Slope Field and Equilibrium Points

Trajectories in the wr-Phase Plane

Other Forms of Species Interaction

9.7 Modeling the Spread of a Disease

Flu in a British Boarding School

The S-I-R model

The Phase Plane

Threshold Value

REVIEW PROBLEMS

STRENGTHEN YOUR UNDERSTANDING

PROJECTS: Harvesting and Logistic Growth, Population Genetics, The Spread of SARS

Focus on Theory

Separation of Variables

The Exponential Growth and Decay Equations

Justification for Separation of Variables

9.1 MATHEMATICAL MODELING: SETTING ...