Citation

Using Maple to apply cubic spline techniques in calculus and mathematical modeling

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Abstract:

The technique inherent in finding a cubic spline can be adapted to fit many applications and to emphasize concepts in various mathematics classes. We will first introduce a Maple worksheet intended for Calculus I students to see how a cubic spline is fit to data points. Students are then asked to alter the cubic spline method to design an initial rise and drop in a roller coaster using their own parameters. This problem is intended to reinforce concepts associated with the derivative that students have recently learned.
We will also discuss how students can use Maple and splines in other courses. For example, cubic splines can be used in Calculus II to approximate the shape of a vase in order to find its volume. In Math Modeling, students are asked to explore multiple techniques to design a high-speed railway route connecting several cities in an optimal way.
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Association:
Name: The Mathematical Association of America MathFest
URL:
http://www.maa.org


Citation:
URL: http://citation.allacademic.com/meta/p377743_index.html
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MLA Citation:

Hollenbeck, Brian. "Using Maple to apply cubic spline techniques in calculus and mathematical modeling" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, Portland Marriott Downtown Waterfront, Portland, OR, Aug 06, 2009 <Not Available>. 2014-11-29 <http://citation.allacademic.com/meta/p377743_index.html>

APA Citation:

Hollenbeck, B. , 2009-08-06 "Using Maple to apply cubic spline techniques in calculus and mathematical modeling" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, Portland Marriott Downtown Waterfront, Portland, OR <Not Available>. 2014-11-29 from http://citation.allacademic.com/meta/p377743_index.html

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: The technique inherent in finding a cubic spline can be adapted to fit many applications and to emphasize concepts in various mathematics classes. We will first introduce a Maple worksheet intended for Calculus I students to see how a cubic spline is fit to data points. Students are then asked to alter the cubic spline method to design an initial rise and drop in a roller coaster using their own parameters. This problem is intended to reinforce concepts associated with the derivative that students have recently learned.
We will also discuss how students can use Maple and splines in other courses. For example, cubic splines can be used in Calculus II to approximate the shape of a vase in order to find its volume. In Math Modeling, students are asked to explore multiple techniques to design a high-speed railway route connecting several cities in an optimal way.


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