Numerical Integration: Discrete Riemann Integrals and Trapezoid Rule

Описание: In this video, I show how to approximate definite integrals to find the area under a curve using discrete numerical methods. In particular, I discuss approximations to the Riemann integral, including left and right rectangle rules, trapezoidal integration, and Simpson's rule based on spline interpolation. Importantly, we discuss the error of each method, compute them in Python and Matlab, and relate these techniques to other intuitive numerical schemes. All with pictures.

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This video was produced at the University of Washington

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0:00 Numerical integration: Discrete Riemann integrals
10:53 Trapezoidal integration
18:42 Simpson's integration rule
22:56 Python code example
26:34 Matlab code example