Guessing the Legendre Polynomial Expansion of a Function

Highlights of the activity

1. This computer visualization activity is designed to help students visualize the expansion of a function via Legendre polynomials.
2. Students use a Maple Worksheet or a Mathematica Notebook to add orthogonal Legendre polynomials and plot the resulting sum, allowing them to understand what it means to add two functions pointwise and to use the guess and check method to find the Legendre expansion of a function.
3. The entire class wrap-up discussion focuses on the geometric meaning of Legendre polynomial series.

Reasons to spend class time on the activity

Legendre fucntions are an important part of the quantum mechanical solution to the hydrogen atom. Students need to become familiar with these functions and with the idea that all functions can be generated from a linear superposition of orthogonal functions. This activity allows students to plot the Legendre functions and practice creating linear combinations of these special functions to create an arbitrary function.

This activity can be used as to reinforce students understanding of Legendre Polynomials and as a good introduction to Legendre Series.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Maple Worksheet

cfguessleg.mw (Maple 13)

cfguessleg.mws (Maple 11 Classic)

Mathematica Notebook

cfguessleg.nb