Differential equations | Generalized functions
In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if is the linear differential operator, then * the Green's function is the solution of the equation , where is Dirac's delta function; * the solution of the initial-value problem is the convolution. Through the superposition principle, given a linear ordinary differential equation (ODE), , one can first solve , for each s, and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of L. Green's functions are named after the British mathematician George Green, who first developed the concept in the 1820s. In the modern study of linear partial differential equations, Green's functions are studied largely from the point of view of fundamental solutions instead. Under many-body theory, the term is also used in physics, specifically in quantum field theory, aerodynamics, aeroacoustics, electrodynamics, seismology and statistical field theory, to refer to various types of correlation functions, even those that do not fit the mathematical definition. In quantum field theory, Green's functions take the roles of propagators. (Wikipedia).
M1D MoDRN Introduction: "Definition of Green Chemistry"
In this module, Prof. Anastas explains the 21-word definition of green chemistry. Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world.
From playlist Introduction to Green Chemistry
M1D MoDRN Introduction: Definition of Green Chemistry
Module 1: Introduction M1D MoDRN Introduction: Definition of Green Chemistry In this module, Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world. In this video, Prof. Anastas
From playlist Introduction to Green Chemistry with Paul Anastas, Module 1
Green's functions: the genius way to solve DEs
Green's functions is a very powerful and clever technique to solve many differential equations, and since differential equations are the language of lots of physics, including both classical mechanics, electrodynamics, and even quantum field theory, so it is important to know how it works.
From playlist Traditional topics, explained in a new way
M1A MoDRN Introduction: "Why Green Chemistry?"
In this module, Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world.
From playlist Introduction to Green Chemistry
M1F MoDRN Introduction: "Green Chemistry's Role in Sustainability"
In this module, Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world.
From playlist Introduction to Green Chemistry
M1F MoDRN Introduction: Green Chemistry's Role in Sustainability
Module 1: Introduction M1F MoDRN Introduction: Green Chemistry's Role in Sustainability In this module, Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world.
From playlist Introduction to Green Chemistry with Paul Anastas, Module 1
M1C MoDRN Introduction: "It is Not My Job"
In this module, Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world.
From playlist Introduction to Green Chemistry
Green's Function In this video, by popular demand, I will derive Green's function, which is a very useful tool for finding solutions of differential equations. Check out my Partial Differential Equations Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCXfuXUAt9dT1Gjy_GK89OH
From playlist Partial Differential Equations
DDPS | Gaining mechanistic insight through learning Green's functions
In this DDPS talk from Aug. 19, 2021, Christopher J. Earls, a Cornell University faculty member in Applied Mathematics, Theoretical and Applied Mechanics, and Civil and Environmental Engineering, discusses using deep neural networks to uncover solutions to hidden partial differential equat
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
L21.3 Integral equation for scattering and Green's function
MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L21.2 Integral equation for scattering and Green's function License: Crea
From playlist MIT 8.06 Quantum Physics III, Spring 2018
Dominika Zgid - A physical/chemical motivation behind quantum embedding theories - IPAM at UCLA
Recorded 09 March 2022. Dominika Zgid presents "A physical/chemical motivation behind quantum embedding theories" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Abstract: The cost of the exact solution of the many-electron problem is believed to be exponen
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022
Excel If Formula - Nested If AND OR Functions
This excel video tutorial provides a basic introduction into the IF Formula. It explains how to use the if function when it's nested with the AND function as well as the OR function. My Website: https://www.video-tutor.net Patreon Donations: https://www.patreon.com/MathScienceTutor Ama
From playlist Excel Tutorial
Lec 34 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 34: Fourier integral transform (part 2) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
C Programming: Image manipulations with arrays
An image is just an array of pixels. We'll apply array algorithms to transform images: darken, flip, mirror, change to grayscale, and more.
From playlist C Programming
This video is feedback on a project for linear algebra. In the project, students were asked to create a growing pixel pattern and analyze it in different ways (height, width, etc).
From playlist BAG PSO PROBLEMS
Calculus 3: Green's Theorem (18 of 21) Using Green's Theorem to Find Area
Visit http://ilectureonline.com for more math and science lectures! In this video I will show how Green's Theorem can sometimes be used to find area of a shape that could be difficult using integration. Next video in the series can be seen at: https://youtu.be/7l2xm1EAzX4
From playlist CALCULUS 3 CH 7 GREEN'S THEOREM
From playlist Exploratory Data Analysis
How the Color Green Increases Creativity I The Great Courses
Brief exposure to the color green enhances our creative output—and nobody knows why. Leading theories involve evolutionary draws to lush vegetation and subconscious approach motivations. Go green and free your inner creative side. Presented by William Lidwell Learn more about how colors a
From playlist Science
Michael Lindsey - Many-body perturbation theory and Green's function methods - IPAM at UCLA
Recorded 10 March 2022. Michael Lindsey of New York University Mathematics presents "Many-body perturbation theory and Green's function methods" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Abstract: Beyond the single-particle picture of density function
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022