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Numerical Calculus Project
Part III/Complete Project
This project will be all about numerical calculus. As you know by now, this project is split into three parts.
You should already have completed the following:
•
Part I: Numerical Differentiation Functions
•
Part II: Numerical Integration Functions
The final part of the project will use the functions from the first two parts and bring them together with an
interface and analysis.
Your Tasks
Task 0: Parts 1 and 2
Begin by making sure your solutions to Parts 1 and 2 of the project are complete and correct, as they are the
foundation to this part of the project.
Create a new project and copy all of the functions from Part 1 and then all of the functions from Part 2.
(Eliminate your test driver main functions.)
As before, your functions
must
be in the order listed in these directions. Do not use prototypes.
Task 1: Function to Analyze
In each prior phase of the project, you analyzed a different function. We'll change our function to a new
function again here, but this time we'll use one that has many practical applications: the standard normal
distribution.
Here is the function for the standard normal distribution:
Of course, integrating this by hand is very difficult, and we'll see how our numerical techniques fare with it.
If you are not familiar with the shape of the graph of this function, use a graphing calculator or some other
utility to view the graph. (You may want to sketch it for your own reference.)
Change your
f
(
x
) function to this function. Find its derivative analytically and adjust your derivative function
accordingly.
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View Full Document Task 2: Error Analysis of the Derivative
We define the
absolute error
of an approximation technique at a point
x
as the absolute value of the
difference in the approximation at
x
and the actual value being approximated at
x
. In other words, if we were
computing the absolute error of the derivative of
f
(
x
), we would simply subtract the actual derivative at
x
from an approximate derivative at
x
.
Create a function that computes the absolute error in an approximation of the derivative of
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This document was uploaded on 02/10/2011.
 Fall '10

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