An equation containing derivatives (rates of change)

			Modeling processes which involve rates of change so that we can successfully predict outcomes

			Physics and engineering are full of differential equations

			Chemistry

			Population growth

			Pollution

			Epidemic

			It's a function which, when substituted into the differential equation, turns the differential equation into an identity.

			is the solution to the differential equation

			The phrase "y is proportional to x" implies that y changes in direct proportion to x, i.e., if x doubles, y doubles, if x triples, y triples.  Functionally, this means y = kx, where k is a constant.  In a similar manner, "y is proportional to the square of x" implies that y = kx2, "y is proportional to the product of x and z" implies y = kxz, and "y is inversely proportional to the cube of x" implies y = k/x3.  For example, when Newton proposed that the force of gravitational attraction of one body to another is proportional to the product of the masses and inversely proportional to the square of the distance between them, he could immediately write: where G is the constant of proportionality, usually known as the universal gravitational constant.  Use these ideas to model each of of the following situations with a differential equation.  All rates are assumed to be with respect to time.

			instantaneous rate of change of a function:  y' = df/dt

			slope of the tangent line to a graph of the function at a particular point

			used in a linear approximation to a function:  y = y(x0) + y'(x)(x-x0)

			limit of the difference quotient:

			Area under the graph of a function

			Antiderivative

			Read Sections 1.1, 1.2 and 1.3.

			Do the exercises on p. 5 (2,6,8,9,10), p. 9 (2,4,6,8,10,12,13,15,16,18,21) and p. 14 (2,4,8,14,18,23,26,28).