Optimization and zeroes of a function
Initial Publication Date: October 14, 2024
Summary
This project is designed for freshman or sophomore undergraduate students to determine the maxima or minima of a function with one variable in an interval using ideas similar to finding the zeroes or the roots of a function.
CollapseLearning Goals
The primary goal is to introduce students to optimization techniques and for the students to be able to find the minimum and maximum values of a function within an interval.
Students learn to program the Bisection method, Newton's method, Secant method, and Interpolation method in MATLAB
Students learn the mathematical analysis of the methods
Context for Use
This activity is a class project for students in a first numerical analysis course. It is assumed that students have basic knowledge of MATLAB programming. The project is assigned to students after being taught how to find Zeroes of a function. Students are also introduced to the Optimization Toolbox in MATLAB.
Description and Teaching Materials
This is a simple numerical method for finding the roots of function and with applications to optimization. It is a project designed to be completed at home within a day or two.
Teaching Notes and Tips
Sample codes can be found in the textbook Numerical Computing with MATLAB: Revised Reprint by Cleve Moler.
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Assessment
1. Students turn in a typed response to the questions posed in the project handout
2. an M-file script
The instructor will run the students' M-files and hand-grade the typed answers.
References and Resources
Numerical Computing with MATLAB: Revised reprint by Cleve Moler, SIAM 2004.
MATLAB Optimization Tool