Interactive Numerical Methods

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Learn by Exploring

Learn more about the numerical algorithms for solving the following types of problems:

• Root Finding
• Bisection
• False Position
• Newton Raphson
• Compare different root finding methods (under construction)
• Curve Fitting
• Linear Regression and Correlation
• Polynomial Curve Fitting (under construction)
• Optimization
• Golden Section Search (under construction)

More About this Project...

The above web-pages for the interactive exploration of numerical methods were created in the spring of 2006 by Prof. Chris Paredis as part of the Class of 1969 Teaching Fellows Program organized by Georgia Tech's Center for the Enhancement of Teaching and Learning. 

The motivation for creating these Java applets grew out of the observation that many students do not get beyond the memorization of the mathematical equations underlying the numerical methods studied in the classroom.  To become proficient in the use of numerical methods, students need to develop a clear understanding of the meaning of these mathematical equations and of the corresponding assumptions and limitations.  In a traditional classroom+homework approach, the students may solve 2-3 problems for each of the numerical methods covered.  Clearly, it is impossible to achieve any level of proficiency based on such a small number of experiences.

The goal of the interactive exploration tools listed above is therefore to increase the number of such experiences dramatically.  The interactive Java applets allow the students to modify the problem (i.e., the data set or function) to which a numerical method is applied in an interactive, graphical fashion.  In the process, they receive immediate feedback on the behavior of the numerical methods.  From the graphical illustrations of the algorithms, the students learn to map the abstract mathematical expressions into graphical, geometric interpretations.  In addition, the students can explore the properties of the algorithms over a wide range of problem instances, allowing them to develop intuition as to:

• which methods work best under which circumstances,
• which assumptions are easily violated, and
• how do the methods behave when the assumptions are violated?

We hope that these applets will complement the theoretical treatment of numerical methods and will help students to become more proficient in the use of computing techniques to solve engineering problems.

Acknowledgements

• Programming assistance was provided by Ivan Lee.
• Funding was provide by Georgia Tech's Center for the Enhancement of Teaching and Learning as part of the Class of 1969 Teaching Fellows Program.
• The Class of 1969 Teaching Fellows Program was organized by Dr. Joyce Weinsheimer who provided guidance and encouragement towards the completion of this project.