Legendre Polynomial Series Coefficients

Highlights of the activity

1. This computer visualization activity is designed to help students visualize the approximation of functions with Legendre polynomials.
2. Students use a Maple Worksheet or a Mathematica Notebook to compute Legendre coefficients, practice approximating a function by adding orthogonal functions, and inspect the region over which the Legendre functions are orthogonal.
3. The entire class wrap-up discussion relates the Legendre polynomial approach in approximating functions to other approaches covered in previous courses (i.e. using Fourier series or power series).

Reasons to spend class time on the activity

Helps build students' geometric understanding of what it means to do eigenfunction expansions. Expands on students' understanding of Fourier Series. Legendre polynomials are fundamental building block towards spherical harmonics.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Maple Worksheet

cflegseries.mw (Maple 13)

cflegseries.mws (Maple 11 Classic)

Mathematica Notebook

cflegseries.nb