Differential calculus | Mathematical analysis

Reduced derivative

In mathematics, the reduced derivative is a generalization of the notion of derivative that is well-suited to the study of functions of bounded variation. Although functions of bounded variation have derivatives in the sense of Radon measures, it is desirable to have a derivative that takes values in the same space as the functions themselves. Although the precise definition of the reduced derivative is quite involved, its key properties are quite easy to remember: * it is a multiple of the usual derivative wherever it exists; * at jump points, it is a multiple of the jump vector. The notion of reduced derivative appears to have been introduced by and Florian Theil in 2004. (Wikipedia).

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I work through 2 example evaluating the limit definition of a derivative. Check out http://www.ProfRobBob.com, there you will find my lessons organized by chapters within each subject. If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my chann

From playlist Calculus (New)

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From playlist CALCULUS 3 CH 4 PARTIAL DERIVATIVES

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From playlist Sect 2.7, Definition of Derivative

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We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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From playlist Sect 2.7, Definition of Derivative

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From playlist Calculus Ch 3 - Derivatives

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From playlist Introduction and Formal Definition of the Derivative

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From playlist Advanced Calculus / Multivariable Calculus

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From playlist Differential Equations

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From playlist Differential Equations

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Click for free access to Educator's best classes: : https://www.unacademy.com/a/Best-Classes-of-all-time-by-Vishvadeep-Gothi-CS.html For regular updates follow : https://unacademy.com/community/Q3ZGJY/ To purchase please click : https://unacademy.onelink.me/081J/zv9co3u1

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From playlist Compiler Design

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From playlist Calculus

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From playlist Introduction and Formal Definition of the Derivative

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Reflexive space | Norm (mathematics) | Lebesgue measure | Bounded variation | Banach space | Radon measure | Mathematics | Separable space | Derivative | Almost everywhere | Continuous function | Sobolev space