Material Detail

This lesson received an honorable mention for the 2011 SoftChalk Lesson Challenge.

'Differential equations show up in many areas of science and technology. In fact, they turn up any time there is a relation involving some continuously varying quantities and ther rates of change. We have actually dealt with differntial equations before. A common modeling problem involving differential equations is the determination of the velocity of a ball falling which has an acceleration which is the acceleration due to gravity minus the acceleration due to air resistance. This is a differential equation because the derivative of the velocity of the ball depends on the velocity, thus finding the velocity as a function of time involves.' solving a differential equation.

'In this section we will

• Examine the basic form of differential equations

• Verify solutions to differential equations

• Determine slope fields for differential equations

• Find solutions to differential equations numerically using Euler's method

• Find solutions to differential equations using seperation of variables.'

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