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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        

Power Curve                            For these curves, 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.

Lab Report Format   Lab Report Rubric   Lab Report Common Mistakes

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Timothy John Beaulieu onto CalculusCourse Projects

CalculusCourse Projects

A collection of projects for students in calculus.

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Timothy John Beaulieu