Exploring errors in approximating definite integrals numerically
This lab is designed to help you investigate how accurate the different standard methods of numerically approximating a definite integral are and how "efficient" each of these is (informally).
WARNING: THIS LAB IS NOT COMPLETE YET. I AM PUTTING IT UP FOR COMMENTS AND FOR MY OWN AMUSEMENT. I WILL EVENTUALLY POLISH THIS UP AND FINISH THE COMMENTARY, BUT THIS IS ALL THERE IS FOR NOW. YOU HAVE BEEN WARNED...
The function and its integral (run this first)
The left and right-hand sums
Defining the Left/Right sums
Error approximation for the Left/Right sums
The Trapezoid and Midpoint rules
Defining the Trapezoid/Midpoint rules
Error approximation for the Trapezoid/Midpoint rules
Simpson's Rule
Defining Simpson's rule
Error approximation for Simpson's rule
Computation times (the cool part)
Created by Mathematica (April 22, 2004)