MAT 227 - Diff Equations with Laplace

1. Solve First-Order Differential Equations
   1. Establish the existence of solutions
   2. Establish the uniqueness of solutions
   3. Graph an approximate solution by using isoclines
   4. Solve Variable Separable differential equations
   5. Solve First-Order Linear differential equations
   6. Solve Exact differential equations
   7. Find Integrating Factors to convert a differential equation to exact
   8. Solve Homogeneous Differential Equations
   9. Reduce differential equations to First Order
   10. Solve application problems involving various of the above
2. Solve Linear Differential Equations
   1. Establish independence of functions by using the Wronskian
   2. Find the characteristic equation of Homogeneous Differential Equations with Constant Coefficients
   3. Solve Euler Differential Equations
   4. Solve differential equations by Reduction of Order
   5. Solve differential equations by the Method of Taylor Series
   6. Solve Nonhomogeneous Differential Equations
   7. Solve differential equations by the Method of Undetermined Coefficients
   8. Solve differential equations by the Method of Variation of Parameter
   9. Solve application problems involving various of the above
3. Solve Linear Systems of Differential Equations
   1. Establish independence by using the Wronskian
   2. Solve differential equations by the Method of Elimination
   3. Solve differential equations by the Matrix Method
   4. Solve Nonhomogeneous Systems by Variation of Parameters
4. Solve by the Laplace Transform
   1. Use the definition of Laplace Transforms to produce formulae
   2. Apply the Laplace Transform and The Inverse Laplace Transform to solve differential equations
   3. Apply the Laplace Transform and The Inverse Laplace Transform to solve systems of differential equations
   4. Solve differential equations using the Heaviside function
   5. Solve differential equations using the Dirac Delta function
5. Solve by using numerical methods
   1. Solve differential equations and systems by using Euler’s method
   2. Solve differential equations and systems by using Taylor Series
   3. Solve differential equations and systems by using the Runge-Kutta method