Assignment For Section 2.4, 2.5, & 2.6
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