Gauss Quadrature

• Write the generic formula for quadrature methods
• With the Trapezoid and Simpson’s methods, we had fixed x-positions. What makes Guass Quadrature special?
• T/F: an n-point Gauss quadrature will be exact for polynomials up to degree $2n$?
• Why is scaling the domain needed when using Gauss Quadratures?
  • How is this done?
• What is the convergence rate of Gauss quadratures with the number of quadrature points?
• Write the formula for Generalized Gauss quadratures in terms of a weight function.
• What is the “full” name of the Gauss quadrature type when the weight function is just $W(z)=1$?
• The soot example given used a generalized quadrature where the particle number density function (the size distribtution) was the weight function. But, when using moment methods, we never actually know what that weight function is. What allows that?