Assignment For Section 1.1

You should first read questions 1-4, and then read section 1 completely. Then you will be ready to answer the reading questions thoroughly. Always keep the answers to the reading questions on a separate piece of paper; these will be randomly collected from time to time.

1)   What is a first-order differential equation? To clarify your definition give several examples which fit your definition and several which do not fit your definition.

2)   Give a real world problem which can be interpreted by a first-order differential equation. Then use the 3-step mathematical modeling described on page 4 to analyze your problem.

3)   Consider example 4 on page 3
a) Explain why there is a negative sign in these differential equations.
b) Are these differential equations first-order differential equation? Explain.

4)   What is an initial value problem? Give an example of an initial value problem which is not of first-order. What is the order of your example and why?

5)   Extend exercise 13-16 on page 9 to determine possible solutions of a differential equation of the form:

where the  represent given constants and  represents the jth derivative of y  with respect to  x. Problems:

page 9     3, 5, 11, 13, 14, 15, 16, 21, 24, 25, 32, 35, 40, 41, 43