Approximate Integration: Trapezoidal Rule Error Bound: Proof скачать в хорошем качестве

Approximate Integration: Trapezoidal Rule Error Bound: Proof

In this video I go over a very extensive proof of the Error Bound formula for the Trapezoidal Rule integration approximation method. In this video I derive an estimate of the error for a single sub-interval using the fact that the integration constant can be chosen to be any number (learn more about this in my next video so stay tuned!). From there I expand the estimate and sum it up for all n-intervals. Now selecting the number K to be at least the maximum value of the absolute value of the second derivative for the given interval, I am able to derive the maximum error bound estimate. In the video I also explain how there are some significant weaknesses in the derivation and show that the actual error can be much less than the maximum error bound estimate. This is a very long and extensive example but it will give you a profound understanding of mathematics and integral approximations in general so make sure to watch the video and follow along if you can! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIheVNl... View Video Notes on Steemit: https://steemit.com/mathematics/@mes/... Related Videos: Approximate Integration: Accuracy and Error Bounds:    • Approximate Integration: Accuracy and Erro...   Approximate Integration: Example 1: 1/x:    • Approximate Integration: Example 1: 1/x   Approximate Integration: Left, Right, Midpoint, and Trapezoidal Rules:    • Approximate Integration: Left, Right, Midp...   The Definite Integral - Brief Introduction:    • The Definite Integral and Riemann Sums: In...   Evaluating Integrals - Examples Part 1 - Using Infinite Rectangles:    • Evaluating Integrals - Examples Part 1 - U...   Evaluating Integrals - Examples Part 2 - Interpreting as Areas:    • Evaluating Integrals - Examples Part 2 - I...   Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison:    • Evaluating Integrals -  Midpoint vs Right ...   Completing the Square:    • Completing the Square   . ------------------------------------------------------ Become a MES Super Fan!    / @mes   DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps