Assignment For Section 2.4, 2.5, & 2.6

**Readings Questions:**

You should read the section before attempting any reading
questions or problems. Remember that you are responsible for all definitions
and examples. **Also remember to keep the answers to the reading questions
on a separate piece of paper; these will be randomly collected from time
to time.**

1) When using Euler's Method for approximating the solution to an initial value problem, can we make our error as small as we want by choosing h sufficiently small? Explain.

2) Chapter 2 discusses three ways to approximate
the solution to an initial value problem: Euler's Method, Improved Euler's
Method, and Runge-Kutta Method.

a)
Compare the number of calculations needed for each method (ie the computer
time cost for using a given method.

b)
Compare the accuracy of each.

c)
Are the extra computations worth the computer expense? Explain.

**Problems:** **page 113
1, 4, 9, 25, 26, 27**
**
page 124 1, 4, 9**
**
page 135 1, 4, 9**