Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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EXPERIMENTS FOR NUMERICAL METHODS

 

Low cost, low space, low setup time experiments have been developed for a course in numerical methods.  Read the following paper to find out how the experiments are being implemented and assessed in the classroom.   

 

The Length of a Curve

 

This experiment illustrates the difference in using curve fitting with polynomial interpolants and spline interpolants. 

 

To the student: A handout is given to the students that gives the background information on the experiment, how to collect the data, and exercises that need to solved.

 

To the Instructor: Do you want to put this experiment together for your class? Find out to see what materials you need to buy, where you can buy the materials, and how much it costs.

 

Experimental Data:  If you do not want to conduct the experiment but want the data.

 

Topics Covered: Interpolation and Integration

 

 

 


Strains in a Loaded Truss

 

This experiment illustrates the use of simultaneous linear equations in finding the forces in the members of a truss. 

 

To the student: A handout is given to the students that gives the background information on the experiment, how to collect the data, and exercises that need to solved.

 

Experimental Data:  If you do not want to conduct the experiment but want the data.

 

Topics Covered: Simultaneous Linear Equations

 

Cooling a Aluminum Cylinder in Iced Water

 

This experiment illustrates several key concepts of numerical methods, mainly regression to find physical constants from the collected data. 

 

To the student: A handout is given to the students that gives the background information on the experiment, how to collect the data, and exercises that need to solved.

 

Experimental Data:  If you do not want to conduct the experiment but want the temperature vs time data.  You will need to look at the handout also to get other needed data.

 

Topics Covered: Regression, Nonlinear Equations, Integration, Ordinary Differential Equations, Differentiation

 

 


Twisting a Mousetrap Spring

This experiment illustrates the concept of regression to find the constants of a linear model of a torsional spring.  Integration is used to find the torsional energy stored in the spring.

'To the student: A handout is given to the students that gives the background information on the experiment, how to collect the data, and exercises that need to solved.

 

Experimental Data:  If you do not want to conduct the experiment but want the forces vs angle data

Topics Covered: Regression, Integration

 

Hold Your Water in a Champagne Glass

 

This experiment illustrates several key concepts of numerical methods, mainly spline interpolation and integration. 

 

To the student: A handout is given to the students that gives the background information on the experiment, how to collect the data, and exercises that need to solved.

 

To the Instructor: Do you want to put this experiment together for your class? Find out to see what materials you need to buy, where you can buy the materials, and how much it costs.

 

Experimental Data:  If you do not want to conduct the experiment but want the radius vs height data

 

Topics Covered: Interpolation, Integration

 

Where is the center - the center of gravity

 

The motivation behind this experiment is to understand spline interpolation and integration to find the center of mass of a thin plate of arbitrary shape

 

To the student: A handout is given to the students that gives the background information on the experiment, how to collect the data, and exercises that need to solved.

 

To the Instructor: Do you want to put this experiment together for your class? Find out to see what materials you need to buy, where you can buy the materials, and how much it costs.

 

Experimental Data:  If you do not want to conduct the experiment but want the height vs length data

 

Topics Covered: Interpolation, Integration

 

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

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