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∫( F )dA = °∫FdL

A L

where,

A,L = A surface area A, with a bounding parimeter of length L

F= a field or vector value over a volume

2.6.3Differential Equations

•Solving differential equations is not very challenging, but there are a number of forms that need to be remembered.

•Another complication that often occurs is that the solution of the equations may vary depending upon boundary or initial conditions. An example of this is a mass spring combination. If they are initially at rest then they will stay at rest, but if there is some disturbance, then they will oscillate indefinitely.

•We can judge the order of these equations by the highest order derivative in the equation.

•Note: These equations are typically shown with derivatives only, when integrals occur they are typically eliminated by taking derivatives of the entire equation.

•Some of the terms used when describing differential equations are,

ordinary differential equations - if all the derivatives are of a single variable. In the example below ’x’ is the variable with derivatives.

e.g.,	d	2	d
	----		x + ----	x = y
	dt		dt

first order differential equations - have only first order derivatives,

e.g.,	d		d
	----	x +	----	y = 2
	dt		dt

second order differential equations - have at least on second derivative,

e.g.,	d	2	d
	----		x + ----	y = 2
	dt		dt

higher order differential equations - have at least one derivative that is higher than second order.