Simpson’s 1/3 Rule Theory & Derivation | Numerical Methods

In this video we're going to unravel the fascinating concept of Simpson’s 1/3 Rule, an essential technique in numerical integration, along with its derivation. Whether you're a student, an enthusiast, or a curious mind seeking to enhance your mathematical understanding, this video is tailored just for you.
Key Points Covered:
- Gain an intuitive grasp of how this rule approximates definite integrals through the division of intervals and quadratic polynomials.
- Dive deep into the derivation process, breaking down the mathematical steps and logic behind Simpson’s 1/3 Rule.
- Receive practical tips and insights for effectively implementing Simpson’s 1/3 Rule in your own numerical integration tasks.
This timeline is meant to help you better understand Simpson’s 1/3 Rule Theory & Derivation:
0:00 Introduction
0:23 Introduction to the Simpson’s 1/3 rule.
2:07 General Definite Integral Of 2nd Order Polynomials
6:06 Developing Simpson’s 1/3 rule.
7:44 Outro
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This video is part of our Numerical Methods course. Numerical methods is about solving math problems through approximating the solution of problems that would be difficult or impossible to solve analytically. In this playlist we will cover topics such as solving systems of linear equations, solving systems of non-linear equations, numerical integration, numerical derivatives, etc..
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[@alphaesports9394]

Hi! Very in-depth, good video. I enjoyed it and you take it one step at a time. One thing to point out, though, is that at around 4:32 when you're setting up the 3rd equation, you're saying that "y_2 = A(y_2)^2 + B(y_2) + C" when it instead should have been "y_2 = A(\delta(x))^2 + B(\delta(x)) + C.
Furthermore, at 4:43, you say to add together equation (1) and equation (2), though that's not what you write on the blackboard. What you write is equation (1) and equation (3) added together. Either way just wanted to give some feedback, but it is definitely a good, clear, concise, and easy-to-follow video, so thank you for that! It helped me a ton with my School Project

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[@FatimaAli-qm3jd]

Thank you, Professor, for this clear and comprehensive explanation of the smallest details. Can you mention the source you relied on to derive Simpson's 1/3 rule.

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