Initial Publication Date: October 21, 2023

# Computation Essay

Lazaros Kikas, , University of Detroit Mercy

Part of my duties in teaching mathematics at the University of Detroit Mercy is to teach the first course of the Calculus sequence. The ideas can be quite complex and abstract. But if the student can see what is going on through a computation, I believe that the concept under discussion can become more clear.

Here is an example. One of my favorite topics to teach in an introductory Calculus course is Newton's method. It is a beautiful iterative method for solving equations and illlustrates well the utility of tangent lines. To implement Newton's method, I have the students use MATLAB. I provide to the student some basic MATLAB code and have them modify code as they go along. To help make connections I have:

(1) Given the student a basic equation to solve so that they can get a feel for how Newton's method works.

(2) Given the student equations with more than root and asked them to justify their choice an initial guess so that Newtons's method converges to the correct root.

(3) Given students an equation that has no root, and ask students to explain why Newton's method diverges.

(4) Given students a problem about, say max/min, and use Newton's method to solve the appropriate equation.

(5) Given students a modified version of Newton, where instead of the derivative, the student uses an approximation of the derivative.

I enjoy giving students these type of projects. But I have noticed somethings:

(1) Students lack programming skills. They have trouble with things like for loops, and if then statements.

(2) Students are sometimes afraid to experiment.

(3) Students lack ability to read graphs to see what is going on with a function.

It is my hope that through this workshop, that I will learn more about MATLAB and its tools, and how I can better use MATLAB in class.