Chapter 02 Numerical Differentiation Divided Differences Simulation

Description:  This simulation depicts the central, backward, and forward divided-difference methods for estimating the first derivative of a set of simple functions.  The student can explore the true errors for each of the methods and see the graphical interpretation of the methods as compared to the exact solution.

Keywords:  differentiation, data, slope, differential calculus, numerical differentiation

Learning Objectives:  After successful completion of running the simulation with proper questions asked by the instructor, the student would be able to 1) infer the effect of step size on the accuracy of central, backward, and forward divided difference methods of estimating the first derivative of a function, 2) infer how effect size affects the accuracy of backward and forward difference methods differently than central divided difference methods of estimating the first derivative of a function.

Full Resources:  The full resources for the topic of numerical differentiation are given here which include textbook content, a PowerPoint presentation, a multiple-choice test, audiovisual lectures, and application examples.

Software Requirements:  Latest versions of Safari,  Microsoft Edge, Firefox, Google Chrome.

Credits:  Design Team: Autar Kaw, Mayank Pandey, Vincent Shatlock.  Software Development: Mayank Pandey.
We acknowledge the immense help of the PhetSims Google group, especially, Michael Kauzmann, Chris Malley, Martin Veillette, Sam Reid, John Blanco, Jesse Greenberg and third party libraries:  almond-0.2.9.js, easing-equations-r12, FileSaver-b8054a2.js, fontawesome-webfont-3.0.2.svg, jama-1.0.2, jquery-2.1.0.js, lodash-2.4.1.js, pegjs-0.7.0.js, seedrandom-2.4.2.js, text-2.0.12.js, Tween-r12.js

Acknowledgments: This material is based upon work supported partially by the National Science Foundation under Grant Number 2013271. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

All Simulations: Here is the link for all the simulations developed.