Integrals | Multiplication | Non-Newtonian calculus
A product integral is any product-based counterpart of the usual sum-based integral of calculus. The first product integral ( below) was developed by the mathematician Vito Volterra in 1887 to solve systems of linear differential equations. Other examples of product integrals are the ( below), the ( below), and some other integrals of non-Newtonian calculus. Product integrals have found use in areas from epidemiology (the Kaplan–Meier estimator) to stochastic population dynamics using multiplication integrals (multigrals), analysis and quantum mechanics. The , together with the , is useful in image analysis and in the study of growth/decay phenomena (e.g., in economic growth, bacterial growth, and radioactive decay). The , together with the bigeometric derivative, is useful in some applications of fractals, and in the theory of elasticity in economics. This article adopts the "product" notation for product integration instead of the "integral" (usually modified by a superimposed "times" symbol or letter P) favoured by Volterra and others. An arbitrary classification of types is also adopted to impose some order in the field. (Wikipedia).
Here I calculate the product derivative, which is the inverse of the product integral introduced in a previous video, and I also share some of its nice properties. Enjoy! Geometric intuition of the product derivative (courtesy MatteHatten): https://youtu.be/pW0Lv7J5DMk Product integral v
From playlist Integrals
ONE WEIRD INTEGRAL! Introducing the PRODUCT INTEGRAL intuitively!
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From playlist Integrals
What is an integral and it's parts
👉 Learn about integration. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which the upper and the lower li
From playlist The Integral
Integral of a product (x - 1)(x + 2)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Integral of a product (x - 1)(x + 2)
From playlist Calculus
Suppose you define the integral, but instead of adding up the values of f, you multiply them. What do you get then? Watch this video and you'll find out! In this video, I define the product integral, and rewrite it in terms of the regular Riemann integral. Then I give a couple of examples,
From playlist Real Analysis
Find the value of the integral with e
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
Evaluate the integral with trig u substitution
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
How to use u substitution to find the indifinite integral
👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as an indefinite integral or as a definite integral. A definite integral is an integral in which t
From playlist The Integral
Use the FTOC to evaluate the integral
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
Lecture 7: Integration (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
How does integration by parts work?
In this video we talk about why the integration by parts formula actually works. What we conclude is that there are two reasons. 0:36 Where does integration by parts come from? // First, the integration by parts formula is a result of the product rule formula for derivatives. In a lot of
From playlist Popular Questions
Mod-01 Lec-12 Gauss 2-point Rule: Construction
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications… - Raphael Beuzart-Plessis
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups Speaker: Raphael Beuzart-Plessis Affiliation: CNRS Date: March 6, 2018 Fo
From playlist Mathematics
V8-5 Tabular Method for integration by parts, examples. Elementary differential equations
V8-5 Tabular Method for integration by parts, examples. Elementary differential equations Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations
Richard Gustavson, Manhattan College
April 26, Richard Gustavson, Manhattan College Developing an Algebraic Theory of Integral Equations
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Calculus - Integration By Parts
This calculus explains how to find the indefinite integral of a 3 product term expression using integration by parts. My Website: https://www.video-tutor.net Patreon Donations: https://www.patreon.com/MathScienceTutor Amazon Store: https://www.amazon.com/shop/theorganicchemistrytutor
From playlist New Calculus Video Playlist
Find the area enclosed by the two curves
Keywords 👉 Learn how to evaluate the integral of a function. The integral, also called antiderivative, of a function, is the reverse process of differentiation. Integral of a function can be evaluated as indefinite integral or as a definite integral. A definite integral is an integral in
From playlist Evaluate Integrals
Calculus 16.7 Surface Integrals
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus