Integrals | Multiplication | Non-Newtonian calculus

Product integral

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).

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Product derivative

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

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ONE WEIRD INTEGRAL! Introducing the PRODUCT INTEGRAL intuitively!

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg Mathvengers: https://www.youtube.com

From playlist Integrals

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👉 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

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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

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Product Integral

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

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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

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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

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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

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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

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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

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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

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From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications… - Raphael Beuzart-Plessis

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From playlist Mathematics

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V8-5 Tabular Method for integration by parts, examples. Elementary differential equations

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From playlist Elementary Differential Equations

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From playlist Spring 2022 Online Kolchin seminar in Differential Algebra

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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

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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

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From playlist Calculus

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