General Course Purpose:

The general purpose is to give the student a solid grasp of the methods solving and applying differential equations and to prepare the student for further coursework in mathematics, engineering, computer science and the sciences.

Course Objectives:

If you successfully complete this course, you will be able to:

First Order Differential Equations

  1. Classify a differential equation as linear or nonlinear.
  2. Understand and create a directional field for an arbitrary first-order differential equation.
  3. Determine the order, linearity or nonlinearity, of a differential equation.
  4. Solve first order linear differential equations.
  5. Solve Separable differential equations.
  6. Solve initial value problems.

Numerical Approximations

  1. Use the Euler or tangent line method to find an approximate solution to a linear differential equation.

Higher Order Differential Equations

  1. Solve second order homogenous linear differential equations with constant coefficients including those with complex roots and real roots.
  2. Determine the Fundamental solution set for a linear homogeneous equation.
  3. Calculate the Wronskian.
  4. Use the method of Reduction of order.
  5. Solve nonhomogeneous differential equations using the method of undetermined coefficients.
  6. Solve nonhomogeneous differential equations using the method of variation of parameters.

Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems

  1. Solve applications of differential equations as applied to Newton's Law of cooling, population dynamics, mixing problems, and radioactive decay. (1st order)
  2. Solve springs-mass-damper, electrical circuits, and/or mixing problems (2nd order)
  3. Solve application problems involving external inputs (non-homogenous problems).

Laplace Transforms

  1. Use the definition of the Laplace transform to find transforms of simple functions
  2. Find Laplace transforms of derivatives of functions whose transforms are known
  3. Find inverse Laplace transforms of various functions.
  4. Use Laplace transforms to solve ODEs.