Newton Method Computation

Lazaros Kikas, University of Detroit Mercy, Mathematics
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Initial Publication Date: October 12, 2023

Summary

This project has the student implement and experiment with the iterative method Newton's Method. Newton's method is a method for solving equations. There is room in this project for the student to experiment with Newton's method and therefore gain further insight.

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Learning Goals

Student will learn here an application of the derivative and the concept of tangent lines so as to approximate the solution to equations. Experimentation is encouraged.
MATLAB code is provided for students to experiment with.
Problems are set up so the student is encouraged to use graphical and analytical skills to solve problems.
Students are expected to explain their solutions in clear and precise language.

Context for Use

This is a first year Calculus level project. Students are expected to understand the derivative and tangent lines. MATLAB knowledge expected in minimum for this project. Sample code is included in the description of the project.

Description and Teaching Materials


Newton Method (Acrobat (PDF) 143kB Oct12 23)



Teaching Notes and Tips

Knowledge of Matlab is minimum for this project. However, for this project students will benefit from an introduction to Matlab, and coding things like for loops.

Assessment

This project is more than just problem solving. Students are expected to write up solutions in a way that explains their thinking. Students are expected to experiment and describe their conclusions. Graphical and analytical methods should be used. Since this is a project, students should have the opportunity to submit preliminary drafts of their work for feedback.

In the end students are graded on the correctness of their work, their explanation of their thinking and on the their creativity in experimenting with Newton's Method.

For instance consider the function $f(x)= 1/(x^2+1)$. This equation has no real solutions. A graph will clearly show this. By applying newton method, the iterations will not converge. The student should see that newton will not converge because there is no root, and because of the graph of $f(x)$ the iterates will grow without bound.

References and Resources

This teaching activity was created as a part of the Teaching Computation with MATLAB Workshop held in 2023 at Carleton College.