MATLAB - Numerical Differentiation @JoelRosenfeld

Uploaded November 2020 | Updated September 2026, 1 week ago

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$Introduction to the Laplace Transform This fast paced video gives an advanced introduction to the Laplace transform for delta functions and distributions. This necessitates the definition of a Schwartz space for the Laplace transform, and it defines the Laplace transform of a distribution through a limit of its action on a particular sequence of functions. //Additional Reading Zemanian - An Introduction to Generalized Functions and the Generalized Laplace and Legendre Transformations (JSTOR) https://www.jstor.org/stable/2027808?seq=1#metadata_info_tab_contents (SIAM) https://epubs.siam.org/doi/abs/10.1137/1010001?journalCode=siread //Exercises - Show that regular functionals defined through functions of exponential type with support in [M,infinity) for some M in R are continuous over L. - Find an explicit function phi in L such that phi is 1 for t less than 1 and 0 for t greater than 2. - Find the Laplace transform of the distribution that maps u in L to its derivative at zero from the definition of Laplace transforms. - Show that the function g(t) = e^{-st} is not in L for any s. //Watch Next The Schwartz Space (Full Lecture) https://youtu.be/StzEO8B1pFY Undergraduate Intro to the Laplace Transform https://youtu.be/mJSqt7nchRQ Introduction to Control Theory https://youtu.be/0v4WFmOm764 What if I were to tell you that the Fourier Transform is not an integral? https://youtu.be/YaeGIgtE6R4 Fixed Point Iteration - Loki gets slapped 16 times for SCIENCE https://youtu.be/_I790SqNDjs //Music Provided by Epidemic Sound Mt Fuji - Oozy Opposite - Jones Meadow Euphoria - Catiso Leaving at Midnight - waykap Pomme - Chantarelle Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel: https://www.epidemicsound.com/referral/644nao //Books Advanced Mathematical Analysis - Beals https://amzn.to/3fn2jdP From Vector Spaces to Function Spaces - Yutaka Yamamoto https://amzn.to/3sU2CVj Feedback Control Theory - Doyle, Francis, Tannenbaum https://amzn.to/3HFvuov Pick Interpolation and Hilbert Function Spaces - Agler and McCarthy https://amzn.to/3EOJU3K Nonlinear Systems - Khalil https://amzn.to/32Zyk8E Modern Control Systems - Dorf and Bishop https://amzn.to/331JQAm Fundamentals of Differential Equations - Nagle, Saff, and Snider https://amzn.to/3qeGD9C //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!$