Department of Mathematics

Math 300: Mathematical Computing

Python ICE 6

Given uniformly spaced points \(a=x_0\lt x_1\lt \dots\lt x_n=b\), with \(x_{i+1}-x_i=h\) for every \(i\), the composite midpoint rule for approximating the integral of a function \(f\) is given by $$ \int_a^b f(x) dx\approx \sum_{i=0}^{n-1} f\left(\frac{x_i+x_{i+1}}{2}\right) h $$ Write a Python function called midpoint to evaluate a midpoint rule approximate to any function \(f\) we specify. We will call the midpoint function as midpoint(f,a,b,n), with arguments as in our other approximate integral functions.


Assignment 6 is posted.




The midterm exam will take place on Friday, 12 October. As always, you are permitted any paper notes you find useful, but no electronic devices are allowed. The test is cumulative, but emphasizes the material covered in the last fours weeks. A sample exam is available.




You need to install Matlab on your computer by Wednesday. You do not need Simulink or any particular toolboxes, though you might find the Symbolic toolbox useful at some time in the future (not in this class).



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