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Homework 3 – Math 104B,

 Homework 3 – Math 104B, Spring 20201

Due on Saturday, April 25th, 2020
Instructor: Carlos J. Garc´ıa Cervera
1. (10 points) Prove that the composite Simpson’s rule is O(h
) when
applied to functions with sufficient derivatives.
2. (10 points) Consider a numerical integration rule of the form
(a) (5 points) What is the linear system that muist be solved in the
method of undetermined coefficients for finding A, B, C? Solve
for A, B, C.
(b) (5 points) What three integrals must be evaluated to determine
A, B, C in a Newton-Cotes formula? Solve for A, B, C.
3. (10 points) Show how the Gaussian quadrature rule
 
i. (5 points) Prove that this approach provides a quadrature
that is second order accurate.
ii. (5 points) Write a program that uses this approach to ap￾proximate (1), and verify the order of accuracy numerically.
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