Preprint Draft, 2012. — 41 pages.
Table of Contents.
Finite Differences and Differential Equations.
Finite Difference Approximation.
The Green’s Function Comparison.
The Role of Interpolation.
Integration by Terms.
Interpolating Polynomials and Influence Functions.
Polynomials in 1 Dimension.
Polynomials in 2 Dimensions.
Visual Interpretation in 2 D.
2 D Interpolation by Opposing Areas.
Introduction to Green’s Functions.
Definition of Green’s Functions.
Electrostatic Green’s Function.
The Magic Rule.
A Simple Explanation of Green’s Functions.
A Three Point Diagram.
The One-Dimensional Solution.
Visual Integration of the Boundary.
A 2D Equivalent of Visual Integration.
Inserting the Propagation Component.
Relationship to General Green’s Functions.
Numerical Green’s Functions.
The Pseudo Green’s Function Approximation.
The Induced Boundary Charge Method.
