Computing with Harmonic Functions

This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral of any polynomial can be computed exactly. Th...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2016-11
Main Author: Axler, Sheldon
Format: Article
Language:English
Subjects:
Computation
Dirichlet problem
Ellipsoids
Harmonic functions
Polynomials
Spherical harmonics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral of any polynomial can be computed exactly. This software can find exact solutions to Dirichlet, Neumann, and biDirichlet problems in R^n with polynomial data on balls, ellipsoids, and annular regions. It can also find bases for spaces of spherical harmonics, compute projections onto the harmonic Bergman space, and perform other manipulations with harmonic functions.
ISSN:2331-8422