Cauchy Schwarz and what to DO with it (corrected) // An Introduction to Real Analysis скачать в хорошем качестве

Cauchy Schwarz and what to DO with it (corrected) // An Introduction to Real Analysis

The Cauchy Schwarz inequality is essential for all of real analysis, and it has several important applications, including the Heisenberg Uncertainty Principle and Normalized Cross Correlation. In this video we give two proofs of the Cauchy Schwarz inequality, and examine an exercise and an application. Thanks to @oʞoʎos and @chaoshengzhe for catching a couple of errors and omissions in the first version of this video. //Books Michael Steele - The Cauchy Schwarz Master Class - https://amzn.to/3jeAny2 Walter Rudin - Principles of Mathematical Analysis 3rd Edition - https://amzn.to/3MDHUis Gerald Folland - Real Analysis: Modern Techniques and Their Applications - https://amzn.to/3JmK6Np R. Shankar - Principles of Quantum Mechanics - https://amzn.to/40825xj Maxwell Rosenlicht - Introduction to Analysis - https://amzn.to/3NFYiAC Tom Apostol - Mathematical Analysis 2nd Edition - https://amzn.to/3mwxFlC //Exercises Can you find another application of Cauchy Schwarz? Scour the internet and share with us in the comments! //MATLAB Code https://bitbucket.org/joelrosenfeld/c... //Watch Next The Real Analysis Survival Guide    • The Real Analysis Survival Guide   Mastering the Art of Reading a Proof: By Example    • Mastering the Art of Reading Proofs: By Ex...   Introduction to Control Theory    • Introduction to Control Theory   //Music Provided by Epidemic Sound Between the Lines - Elijah N Beach Memories - Sum Wave bam. bam. - Yomoti Step it up - Riverworm Future Vibes - Qeeo Quixotic - Jobii Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel: https://www.epidemicsound.com/referra... //Recording Equipment Canon SL3: https://amzn.to/3nZ11KU Canon T6i: https://amzn.to/3FUpkQh Rode VideoMic: https://amzn.to/3lhldGa Blue Yeti Microphone: https://amzn.to/3I1y88N Yeti Nano Microphone: https://amzn.to/3I1mriA SanDisc 256GB SD Card: https://amzn.to/3E3LOOr Neewer 5600K USB LED Lights: https://amzn.to/3xvB9cN Neewer 18 inch Ring Light: https://amzn.to/2ZvgCsc Camera Power Adapter: https://amzn.to/3D3upUu DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you! 0:00 Introduction 1:21 First Proof 4:32 Use Example 5:51 Second Proof 10:36 Normalized Cross Correlation 12:32 Wrap Up