CONTENTS
1.1 Mathematical Models, Solutions, and Direction Fields
1.2 Linear Equations: Method of Integrating Factors
1.3 Numerical Approximations: Euler’s Method
1.4 Classification of Differential Equations
First Order Differential Equations
2.2 Modeling with First Order Equations
2.3 Differences Between Linear and Nonlinear Equations
2.4 Autonomous Equations and Population Dynamics
2.5 Exact Equations and Integrating Factors
2.6 Accuracy of Numerical Methods
2.7 Improved Euler and Runge–Kutta Methods
2.P.1 Harvesting a Renewable Resource
2.P.2 Designing a Drip Dispenser for a Hydrology Experiment
2.P.3 A Mathematical Model of a Groundwater Contaminant Source
2.P.4 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin
Systems of Two First Order Equations
3.1 Systems of Two Linear Algebraic Equations
3.2 Systems of Two First Order Linear Differential Equations
3.3 Homogeneous Linear Systems with Constant Coefficients
3.6 A Brief Introduction to Nonlinear Systems
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