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| Introduction | |
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| Some Basic Mathematical Models | |
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| Direction Fields | |
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| Solutions of Some Differential Equations | |
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| Numerical Approximations: Euler's Method | |
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| Classification of Differential Equations | |
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| First Order Differential Equations | |
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| Linear Equations | |
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| Method of Integrating Factors | |
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| Separable Equations | |
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| Modeling with First Order Equations | |
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| Differences Between Linear and Nonlinear Equations | |
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| Autonomous Equations and Population Dynamics | |
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| Exact Equations and Integrating Factors | |
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| Accuracy of Numerical Methods | |
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| Improved Euler and Runge-Kutta Methods | |
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| Summary | |
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| Projects | |
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| Harvesting a Renewable Resource | |
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| Designing a Drip Dispenser for a Hydrology Experiment | |
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| A Mathematical Model of a Groundwater Contaminant Source | |
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| Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin | |
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| Systems of Two First Order Equations | |
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| Systems of Two Linear Algebraic Equations | |
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| Systems of Two First Order Linear Differential Equations | |
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| Homogeneous Linear Systems with Constant Coefficients | |
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| Complex Eigenvalues | |
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| Repeated Eigenvalues | |
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| A Brief Introduction to Nonlinear Systems | |
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| Numerical Methods for Systems of First Order Equations | |
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| Summary | |
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| Projects | |
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| Eigenvalue-Placement Design of a Satellite Attitude Control System | |
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| Estimating Rate Constants for an Open Two-Compartment Model | |
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| The Ray Theory of Wave Propagation | |
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| A Blood-Brain Pharmacokinetic Model | |
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| Second Order Linear Equations | |
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| Definitions and Examples | |
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| Theory of Second Order Linear Homogeneous Equations | |
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| Linear Homogeneous Equations with Constant Coefficients | |
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| Characteristic Equations with Complex Roots | |
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| Mechanical and Electrical Vibrations | |
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| Nonhomogeneous Equations | |
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| Method of Undetermined Coefficients | |
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| Forced Vibrations, Frequency Response, and Resonance | |
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| Variation of Parameters | |
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| Summary | |
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| Projects | |
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| A Vibration Insulation Problem | |
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| Linearization of a Nonlinear Mechanical System | |
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| A Spring-Mass Event Problem | |
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| Uniformly Distributing Points on a Sphere | |
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| Euler-Lagrange Equations | |
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| The Laplace Transform | |
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| Definition of the Laplace Transform | |
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| Properties of the Laplace Transform | |
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| The Inverse Laplace Transform | |
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| Solving Differential Equations with Laplace Transforms | |
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| Discontinuous Functions and Periodic Functions | |
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| Differential Equations with Discontinuous Forcing Functions | |
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| Impulse Functions | |
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| Convolution Integrals and Their Applications | |
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| Linear Systems and Feedback Control | |
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| Summary | |
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| Projects | |
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| An Electric Circuit Problem | |
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| Effects of Pole Locations on Step Responses of Second Order Systems | |
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| The Watt Governor, Feedback Control, and Stability | |
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| Systems of First Order Linear Equations | |
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| Definitions and Examples | |
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| Basic Theory of First Order Linear Systems | |
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| Homogeneous Linear Systems with Constant Coefficients | |
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| Complex Eigenvalues | |
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| Fundamental Matrices and the Exponential of a Matrix | |
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| Nonhomogeneous Linear Systems | |
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| Defective Matrices | |
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| Summary | |
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| Projects | |
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| A Compartment Model of Heat Flow in a Rod | |
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| Earthquakes and Tall Buildings | |
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| Controlling a Spring-Mass System to Equilibrium | |
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| Nonlinear Differential Equations and Stability | |
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| Autonomous Systems and Stability | |
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| Almost Linear Systems | |
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| Competing Species | |
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| Predator-Prey E | |