The successes of the differential equation paradigm were impressive and extensive. Many problems, including basic and important ones, led to equations that could be solved. A process of self-selection set in, whereby equations that could not be solved were automatically of less interest than those that could.

Ian Stewart

sections:

      6.1, 6.2, 6.3, and 6.4

The major value for calculus in applied areas is to set up and solve differential equations. These equations involve rates of change—derivatives. Often realty can be easily modeled in terms of differential equations.

objectives:

• define the term differential equation
• describe what constitutes a solution
• distinguish between a general solution and a singular solution
• verify solutions
• define a solution curve
• explain how intial conditions lead to a particular solution
• sketch a slope field
• use Euler's method
• solve a differntial equation by separation of variables
• use exponential functions
• define what is meant by a homogeneous solution
• solve homogeneous equations by substitution
• use and solve the logistic equation
• define the order of a differential equation
• identify the order of a differential equation
• find and utilize an integrating factor
• use and solve a Bernoulli equation