Math 151a Notes, Fall 2014
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They are pdf files.

Basic Quadrature Methods (4 December version)
 Riemann Sums:
Uniform Subintervals
 LeftHand and RightHand Rules:
Error Bounds for Monotonic Integrands,
Asymptotic Error.
 Midpoint and Trapezoidal Rules:
Error Bounds for Convex and Concave Integrands,
Asymptotic Error.
 Simpson Rule:
Relation to Midpoint and Trapezoidal Rules,
Asymptotic Error.
 Error Estimates for Quadrature Methods:
LeftHand and RightHand Rules, Midpoint Rule,
Trapezoidal Rule, Simpson Rule.

Gauss Quadrature Methods (8 December version)
 Introduction:
Posing the Question of Maximum Precision.
 Quadrature Weights:
Formulas for Quadrature Weights in Terms of
Quadrature Points.
 Maximum Possible Precision:
Expected Maximum Precision,
Upper Bound on Precision.
 Orthogonality Condition:
Characterization of Precision.
 Orthogonal Polynomials:
Construction of Orthogonal Polynomials,
Simple Roots.
 Gaussian Quadrature Sets:
Recipe from Orthogonal Polynomials,
Positivity of Gaussian Quadrature Weights,
Three Examples