L5-6: harmonics etc

Question 1

quadrature scheme

Answer 1

approximating an integral as a summation

Question 2

Gauss-Legendre quadrature scheme (vs basic summation)

Answer 2

for integrals between -1 and 1, can change variables to apply elsewhere etc

lower error for every value of n, saves computing power

Question 3

Laplacian operator

Answer 3

divergence

upside down triangle, squared

shows rate of change

Question 4

spherical harmonics + expansions: Fourier series

Answer 4

periodic function is put in terms of sin + cos functions

Question 5

spherical harmonic functions are defined through …

Answer 5

solution of the eigenvalue problem

equation with Y, l, m,

Question 6

uses of spherical harmonic functions

Answer 6

can be used to expand an arbitrary function on the unit sphere

Question 7

Fourier transform

Answer 7

Fourier transform converts signal from time domain to frequency domain

Question 8

fast spherical harmonic transformation

Answer 8

based on numerical quadrature schemes

made more efficient by application of the FFT algorithm