Includes index.

Website to support book: http://www.wiley.com/college/brannan.

1. Introduction. 1.1 Some Basic Mathematical Models; Direction Fields. 1.2 Solutions of Some Differential Equations. 1.3 Numerical Approximations: Euler's Method. 1.4 Classification of Differential Equations. 2. First Order Differential Equations. 2.1 Linear Equations; Method of Integrating Factors. 2.2 Separable Equations. 2.3 Modeling with First Order Equations. 2.4 Differences Between Linear and Nonlinear Equations. 2.5 Autonomous Equations and Population Dynamics. 2.6 Exact Equations and Integrating Factors. 2.7 Accuracy of Numerical Methods. 2.8 Improved Euler and Runge-Kutta Methods. Summary. Projects. 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. 3. 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. 3.4 Complex Eigenvalues. 3.5 Repeated Eigenvalues. 3.6 A Brief Introduction to Nonlinear Systems. 3.7 Numerical Methods for Systems of First Order Equations. Summary. Projects. 3.P.1 Eigenvalue-Placement Design of a Satellite Attitude Control System. 3.P.2 Estimating Rate Constants for an Open Two-Compartment Model. 3.P.3 The Ray Theory of Wave Propagation. 3.P.4 A Blood-Brain Pharmacokinetic Model. 4. Second Order Linear Equations. 4.1 Definitions and Examples. 4.2 Theory of Second Order Linear Homogeneous Equations. 4.3 Linear Homogeneous Equations with Constant Coefficients. 4.4 Characteristic Equations with Complex Roots. 4.5 Mechanical and Electrical Vibrations. 4.6 Nonhomogeneous Equations; Method of Undetermined Coefficients. 4.7 Forced Vibrations, Frequency Response, and Resonance.

Differential Equations: An Introduction to Modern Methods and Applications is a textbook designed for a first course in differential equations commonly taken by undergraduates majoring in engineering or science. It emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. Section exercises throughout the text are designed to give students hands-on experience in modeling, analysis, and computer experimentation. Optional projects at the end of each chapter provide additional opportunities for students to explore the role played by differential equations in scientific and engineering problems of a more serious nature.