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
- Classify a differential equation as linear or nonlinear.
- Understand and create a directional field for an arbitrary first-order differential equation.
- Determine the order, linearity or nonlinearity, of a differential equation.
- Solve first order linear differential equations.
- Solve Separable differential equations.
- Solve initial value problems.
Numerical Approximations
- Use the Euler or tangent line method to find an approximate solution to a linear differential equation.
Higher Order Differential Equations
- Solve second order homogenous linear differential equations with constant coefficients including those with complex roots and real roots.
- Determine the Fundamental solution set for a linear homogeneous equation.
- Calculate the Wronskian.
- Use the method of Reduction of order.
- Solve nonhomogeneous differential equations using the method of undetermined coefficients.
- Solve nonhomogeneous differential equations using the method of variation of parameters.
Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
- Solve applications of differential equations as applied to Newton's Law of cooling, population dynamics, mixing problems, and radioactive decay. (1st order)
- Solve springs-mass-damper, electrical circuits, and/or mixing problems (2nd order)
- Solve application problems involving external inputs (non-homogenous problems).
Laplace Transforms
- Use the definition of the Laplace transform to find transforms of simple functions
- Find Laplace transforms of derivatives of functions whose transforms are known
- Find inverse Laplace transforms of various functions.
- Use Laplace transforms to solve ODEs.