Topics include:  First order ordinary differential equations (existence and uniqueness of solutions, solution techniques, direction fields and stability, modeling applications); Second and higher order linear equations (existence and uniqueness, fundamental set of solutions of homogeneous equations, Wronskian, reduction of order, equations with constant coefficients, method of undetermined coefficients, method of variation of parameters, solutions in series, Laplace transform method, modeling applications); Systems of linear differential equations (existence and uniqueness of solutions, eigenvalue method for homogeneous systems, method of variation of parameters for systems, Laplace transform method for systems, modeling applications). An introduction to nonlinear systems will be covered as well.

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• Identify, analyze and subsequently solve physical situations whose behavior can be described by ordinary differential equations.
• Determine solutions to first order separable differential equations.
• Determine solutions to first order linear differential equations.
• Determine solutions to first order exact differential equations.
• Determine solutions to second order linear homogeneous differential equations with constant coefficients.
• Determine solutions to second order linear non-homogeneous differential equations with constant coefficients.

1. Differential Equations With Applications and Historical Notes by George F. Simmons
2. A First Course in Differential Equations by Dennis G. Zill

Biweekly Quiz, One Midterm Exam, One Final Exam, Project