STAMP and the Calculus

John Kauffman

I'm thinking through a short course for high school students that would use STAMP projects to illustrate concepts in high school math. Or, to think conversely, use math to enhance understanding of STAMP projects.
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The basics lay out pretty well. For example:
- use a simple link attached to a servo to illustrate trig functions to calculate the link's horizontal travel from a given pulse width
- use a set of resistive values from a photoresistor to create an equation of y=mx+b
Let me know if you want to see the outline in its rough form (at this point just general ideas for topics & projects)
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The students will have:
- WAM text and kit
- Floating point coprocessor (uM-FPU V2 Parallax part #604-00030a) or we might do this seminar without coprocessors
- I could add a component or two if they could make a good project
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The students have done all of WAM and most have done something more with Stamps (BAaD, BoeBOT or SX/B)
The students are at different levels of high school, but for the question below the readers will have completed or be half-way through high school calculus.
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At this point I am looking for examples in two areas:
Calculus - a project illustrating differentiation
Calculus - a project illustrating integration
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Has anyone used calculus in a project or has an idea for a simple project that could be used to demonstrate differentiation and integration with the STAMP? Even rough ideas would be fine, I can probably chew them into something usable.
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Thanks.
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bobledoux

The Parallax Industrial Control module introduces PID techniques using a 35mm film canister, heating resistor, and a temperature sensor. PID stands for Proportional, Integral, and Differential.

Using a loop routine, differential measures are demonstrated by taking change in temperature between loops.

Integral measures are demonstrated by summing temperature errors over a series of loops.

The concepts are displayed using StampPlot lite.

Look at it here: The manual is a free download.

http://www.parallax.com/detail.asp?product_id=28156

Aristides Alvarez

Hi John,

I recommend you to visit this link:

http://www.emesys.com/BS2index.htm#math

Maybe it doesn't have exactly what you're looking for but it has a lot of Math resources generated by Tracy Allen.



Regards,

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Aristides Alvarez
Education and Technical Support Manager
aalvarez@parallax.com
Parallax, Inc. www.parallax.com

claylj

There is a nice posting in the Stamps in Class forum on PID at the URL below.

Larry

http://forums.parallax.com/showthread.php?p=529609

Paul Baker

Since calculus is based on symbolic manipulations, microcontrollers are ill suited to do straight calculus. However the computational approach, numerical analysis, is possible. http://www.computerscilibrary.com/EmbeddedSystems.html·is a good source for sites that discuss the topic, in the left frame scroll down to Numerical Analysis section, they have 40 links to sites that cover the topic.

Tracy Allen

The RCTIME command offers good possibilities to introduce calculus. You have a first order differential equation for charging a capacitor. The capacitor integrates the current. The Stamp introduces a threshold. The Stamp is not _doing_ calculus, but a little simple calculus helps greatly to understand how the command works.

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Tracy Allen
www.emesystems.com

allanlane5

I think it's called 'Discrete Math'. This is calculus that does not divide down the Delta-X until it is infinitely small. Instead it divides the Delta-X down to a small value -- then uses the 'Y' values at the Delta-X 'sample-times'. PID algorithms are based on this math.

Oh, and you CAN have integrators and derivators made out of op-amps and capacitors, as Tracy said above, and monitor their outputs with the BS2.