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#### Average Value of weighted functions

This project applies a lot of integration techniques:

Using the mathematics discussed in class: finding average value of a function with probabilistic inputs.  You are to come up with an extension to the wind the wind turbine problem done in class.  You may either find wind data for a new site or find a new power curve .  Or you might look for data for other kinds of energy production.  Weighted functions are not unique to power generation though.  The average of any function, f, with probabilistic input , pdf p, is

A=-f(x)(x)dx.

http://t.co/MCz9LEKf has a quick summary of weighted functions in computing energy as a result of wind power generation.  Here is our data from the activity from class. More info

If input cannot be found as a probability, (if the area under the input curve is not 1), then w(t) is a weight, and we calculate the average as

A=abf(x)w(x)dxabw(x)dx.

MIT Open Course has a tutorial on general weighted functions with a “non-power” related application.  Other applications can be found in center of mass and mean phenotype as a result of artificial selection.

You may work in groups to research your idea if you have a partner with similar interests, but each person must write their own report with their own scientific questions.  Your idea with some preliminary background research is due as a ppt next class.  If you are working in a group, each member’s subproject should be clear.  The class will discuss and critique and the each member will write his/her scope of work as a lab report due the Wednesday after break.

Category                                                   Points

HW Part & Action plan                                 13% (10 points)

(Present in ppt form to class Wed before break, needs references, detailed data)

Lab report draft due Sunday (to peer) Wednesday after break            20% (12 points)

Peer review feedback due Friday, Plan for revision due Sunday        17% (8 points)

Lab report, due following Friday                         50% (30 points)

Background Research

Distribution Curve                  To fit a distribution curve, you may need this JMP tutorial

Calculation

Meaning and significance

The lab research report will be graded using the Center for Biodiversity Research report rubric.

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Timothy John Beaulieu onto CalculusCourse Projects

#### CalculusCourse Projects

A collection of projects for students in calculus.

6 posts

Timothy John Beaulieu

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