Brannan provides engineers with both an introduction to, and a survey of, modern methods, applications, and theory of a powerful mathematical apparatus that will help them in the field. Section exercises of varying levels of difficulty give them hands-on experience in modeling, analysis, and computer experimentation. New coverage is included on series solutions of second order linear equations, partial differential equations and Fourier Solutions, and boundary value problems and Sturm-Liouville Theory. The companion ODE Architect CD arms them with a user-friendly software tool for computing numerical approximations to solutions of systems of differential equations, and for constructing component plots, direction fields, and phase portraits. Physical representations of dynamical systems and animations available in the ODE Architect enable engineers to visualize solutions routinely.

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1. Introduction 2. First Order Differential Equations 3. Systems of Two First Order Equations 4. Second Order Linear Equations 5. The LaPlace Transform 6. Systems of First Order Linear Equations 7. Nonlinear Differential Equations and Stability 8. Series Solutions of Second Order Linear Equations 9. Partial Differential Equations and Fourier Series 10. Boundary Value Problems and Sturm-Liouville Theory A. Matrices and Linear Algebra B. Complex Variables Answers to Selected Problems References Index