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.

The last test will take place at the final exam time on Tuesday, 12 December, from 1:30-3:30. It will be written as a one-hour (not 50 minute) exam, but you may have the full two hours for it. In other respects it will be very like the other tests, but comprehensive - it will emphasize Python, but cover all the topics we have seen. There is a Sample Exam, but be aware that things will have changed somewhat with the advent of ChatGPT.

Assignment A is posted.

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