MATLAB Explorations

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. Two sample assignments are included. One is a brief introductory assignment for students in their first Numerical Analysis class to use the plot commands in MATLAB to review and expand their understanding of Taylor polynomials. The other requires the student to discover the smallest positive number and largest positive number that can be represented on their computer.

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Learning Goals

The main goals of these exercises are to use MATLAB to explore visually the properties of Taylor polynomials and to explore the numerical limits of a computer.
The objectives are:
1.) Initiate the students' use of MATLAB to explore mathematical concepts;
2.) Strengthen and enhance the students' expertise with MATLAB, especially the plot commands;
3.) Graphically/visually investigate the properties of Taylor polynomials; and
4.) Understand the numerical limits of a computer.

Context for Use

The two sample take-home assignments are intended for an upper level undergraduate/first year graduate Numerical Analysis course. The students should have studied Taylor polynomials in calculus. Although programming is a prerequisite for most Numerical Analysis courses most, if not all, students may not have used MATLAB. They are 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.

These short introductory assignments encourage students to use computation to investigate mathematical concepts.

Description and Teaching Materials

The MATLAB Exploration I assignment, "Exploring Taylor Polynomials with MATLAB", is distributed on the first day of class. It is explained and Taylor polynomials discussed in class. The solution is due at the beginning of the next class meeting.

After the theoretical numerical limits of a computer are discussed in class, MATLAB Exploration II, "Use MATLAB to Explore the Numerical Limits of Your Computer" is assigned. The solution is due in one week.
MATLAB Exploration I: Exploring Taylor Polynomials with MATLAB (Acrobat (PDF) 111kB Aug16 18)
MATLAB Exploration II: Use MATLAB to Explore the Numerical Limits of Your Computer (Acrobat (PDF) 77kB Aug16 18)


Teaching Notes and Tips

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.