MATH 4347 – Introduction to PDE (Harrell)

11/11/11 Triple prime time for a review

Copyright 2011 by Evans M. Harrell II.

MATH 4347 – Introduction to PDE (Harrell)

11/11/11 Triple prime time for a review

Copyright 2011 by Evans M. Harrell II.

WHAT’S THE TEST ALL ABOUT? • ZT, Chapter 6. • ZT, Chapter 7, §§1-4, 5 (except representation theorem), 6, 7 (except Poisson’s integral), 8. • ZT, Chapter 9, §§1-2. • Related parts of HH.

New harmonic functions from old

  reflections   rotations   similarities (scale by λ)   For R2, inversion through the circle rr* = a2.

  strange fact: If u(r,θ) is harmonic, then so is u*(r*,θ) = u(a2/r*,θ) (2D) or (a/r*) u(a2/r*,θ) (3D)

Who invented the Dirac Delta function?