
MAT 227  Diff Equations with Laplace Credits: 4 Lecture Hours: 4 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: Core Ordinary differential equations, systems of ordinary differential equations, Laplace transforms, numerical methods and applications. Prerequisite: MAT 217 or equivalent with a C or better Competencies
 Solve FirstOrder Differential Equations
 Establish the existence of solutions
 Establish the uniqueness of solutions
 Graph an approximate solution by using isoclines
 Solve Variable Separable differential equations
 Solve FirstOrder Linear differential equations
 Solve Exact differential equations
 Find Integrating Factors to convert a differential equation to exact
 Solve Homogeneous Differential Equations
 Reduce differential equations to First Order
 Solve application problems involving various of the above
 Solve Linear Differential Equations
 Establish independence of functions by using the Wronskian
 Find the characteristic equation of Homogeneous Differential Equations with Constant Coefficients
 Solve Euler Differential Equations
 Solve differential equations by Reduction of Order
 Solve differential equations by the Method of Taylor Series
 Solve Nonhomogeneous Differential Equations
 Solve differential equations by the Method of Undetermined Coefficients
 Solve differential equations by the Method of Variation of Parameter
 Solve application problems involving various of the above
 Solve Linear Systems of Differential Equations
 Establish independence by using the Wronskian
 Solve differential equations by the Method of Elimination
 Solve differential equations by the Matrix Method
 Solve Nonhomogeneous Systems by Variation of Parameters
 Solve by the Laplace Transform
 Use the definition of Laplace Transforms to produce formulae
 Apply the Laplace Transform and The Inverse Laplace Transform to solve differential equations
 Apply the Laplace Transform and The Inverse Laplace Transform to solve systems of differential equations
 Solve differential equations using the Heaviside function
 Solve differential equations using the Dirac Delta function
 Solve by using numerical methods
 Solve differential equations and systems by using Euler’s method
 Solve differential equations and systems by using Taylor Series
 Solve differential equations and systems by using the RungeKutta method
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