MATLAB Explorations: Use MATLAB to Explore Lagrange Polynomials

Joan Weiss, Fairfield University, Mathematics
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Summary

"MATLAB Exploration" assignments encourage students to use MATLAB as a tool to explore mathematical concepts. The goal of the attached sample assignment is to guide students to investigate the behavior of Lagrange polynomials.

Learning Goals

The main goals of this MATLAB Exploration exercise are to use MATLAB to explore visually the properties of Lagrange polynomials

The objectives are:
  1. Extend the students' use of MATLAB to explore mathematical concepts;
  2. Strengthen and enhance the students' expertise with MATLAB, especially the plotting/graphing commands; and
  3. Graphically/visually investigate the properties of Lagrange polynomials.

Context for Use

The sample take-home assignment is intended for an upper level undergraduate/first year graduate Numerical Analysis course. In class the students should have been introduced to Lagrange polynomials. Although programming is a prerequisite for most Numerical Analysis courses most, if not all, students may not have used MATLAB. They have been encouraged to spend a few hours at a link like:

Getting started with MATLAB (Mathworks)

http://www.mathworks.com/help/matlab/getting-started-with-matlab.html

or going through the beginning lessons in a text like Getting Started with MATLAB, Seventh by Rudra Pratap.

This was the third assignment to encourage students to use computation to investigate mathematical concepts.

Description and Teaching Materials

Assessment

Each student's solution will be assessed for correctness.

References and Resources

Getting started with MATLAB (Mathworks)
http://www.mathworks.com/help/matlab/getting-started-with-matlab.html

Getting Started with MATLAB, Seventh, Pratap, Rudra, Oxford University Press, 2017.

Numerical Analysis, Tenth, Burden, Richard L., Faires, J. Douglas and Burden, Annette M., Cengage Learning, 2016.