STANDARD COMPETENCIES:

 

 1.   Recognize and classify differential equations and determine when unique solutions exist.

 2.   Solve first order differential equations including separable equations, linear equations, and exact equations.

 3.   Find Wronskian determinants and use these to prove linear independence.

 4.   Recognize and find the general solution of homogenous and non-homogeneous equations.

 5.   Solve differential equations using operators.

 6.   Solve differential equations where the auxiliary equation has (a) distinct roots, (b) repeated roots, and (c) imaginary roots.

 7.   Solve linear nonhomogeneous equations using (a) the methods of undetermined coefficients, (b) the method of reduction of order, (c) the method of and variation of parameters, and (d) the operator 1/f(D).

 8.   Define and find the Laplace transforms of elementary functions, exponential functions, periodic functions, and derivatives.

 9.   Find the derivatives of Laplace transforms.

 10. Find and use an inverse Laplace transform to find a function.

 11. Solve equations, applications, and systems using Laplace transforms and inverse transforms.

 12. Solve homogenous systems with constant coefficients.

 13. Solve Systems of linear differential equations using the Laplace transform.

 14. Use power series to represent linear differential equation.

 TOPICAL OUTLINE:

 

 I.      First Order Differential Equations: Separation of Variables, Exact Equations, Integrating Factors

 II.     Linear Differential Equations: Linear Independence, Homogenous Equations, Nonhomogeneous Equations, and Differential Operators.

 III.    Linear Equations with Constant Coefficients: Auxiliary equations; distinct roots, Auxiliary equations; repeated roots, and Auxiliary equations; imaginary roots.

 IV.     Nonhomogeneous Equations: Method of undetermined coefficients,  Method of reduction of order, and Method of variation of parameters.

 V.      Inverse differential operators:  The operator 1/f(D).

 VI.     Laplace Transforms: elementary functions Transforms of, Inverse transforms, and Inverse transforms.

 VII.    Linear systems of Equations:  Homogenous systems with constant Coefficients, Nonhomogeneous systems, and Systems of linear equations and the Laplace transform.

 VIII.   Power series solutions:  Linear differential equations and power series.