Real analysis | Generalizations of the derivative

Dini derivative

In mathematics and, specifically, real analysis, the Dini derivatives (or Dini derivates) are a class of generalizations of the derivative. They were introduced by Ulisse Dini, who studied continuous but nondifferentiable functions. The upper Dini derivative, which is also called an upper right-hand derivative, of a continuous function is denoted by f and defined by where lim sup is the supremum limit and the limit is a one-sided limit. The lower Dini derivative, f, is defined by where lim inf is the infimum limit. If f is defined on a vector space, then the upper Dini derivative at t in the direction d is defined by If f is locally Lipschitz, then f is finite. If f is differentiable at t, then the Dini derivative at t is the usual derivative at t. (Wikipedia).

Video thumbnail

What is the Derivative?

Derivatives are the main object of study in differential calculus. They describe rates of change of functions. That makes them incredibly useful in all of science, as many models can be expressed by describing the changes over time (e.g. of physical quantities). However, the abstract defin

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Definition of derivative in terms of a limit, (def 1)

Definition of derivative, calculus 1 homework solution. #calculus Check out my 100 derivatives: https://youtu.be/AegzQ_dip8k

From playlist Sect 2.7, Definition of Derivative

Video thumbnail

definition of derivative for a rational function

Here we will use the definition of derivative to find the derivative of a rational function. This is a slightly harder calculus 1 problem so be sure you practice it a few times and make sure you can do it on your own. Get a derivative t-shirt: 👉 https://bit.ly/derivativetshirt Use "WELCO

From playlist Sect 2.7, Definition of Derivative

Video thumbnail

SHM 18/10/2019 - Étudier Ulisse Dini : entre mathématiques et vie politique - Bottazzini

Bottazzini (Università degli studi di Milano) / 18.10.2019 Étudier Ulisse Dini : entre mathématiques et vie politique ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenri

From playlist Séminaire d'Histoire des Mathématiques

Video thumbnail

Evaluating Limits Definition of Derivative

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)

Video thumbnail

Calculus - What is a Derivative? (1 of 8) Overview

Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general overview and the definition of “What is a derivative?”

From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?

Video thumbnail

Find a Derivative Using The Limit Definition (Rational Function: Linear/Linear)

This video explains how to find the derivative of a rational function using the limit definition.

From playlist Introduction and Formal Definition of the Derivative

Video thumbnail

Where Does the Definition of the Derivative Come From?

A student asked about the definition of the derivative in class so I derived the definition really quickly. We had just finished covering infinite limits so we were not talking about derivatives yet, but it was such a good question that I thought I should share this here. I hope this hel

From playlist Calculus 1 Exam 1 Playlist

Video thumbnail

Optimal Transportation and Applications - 13 November 2018

http://crm.sns.it/event/436 It is the ninth edition of this "traditional'' meeting in Pisa, after the ones in 2001, 2003, 2006, 2008, 2010, 2012, 2014 and 2016. Organizing Committee Luigi Ambrosio, Scuola Normale Superiore, Pisa Giuseppe Buttazzo, Dipartimento di Matematica, UniversitĂ 

From playlist Centro di Ricerca Matematica Ennio De Giorgi

Video thumbnail

Optimal Transportation and Applications - 15 November 2018

http://crm.sns.it/event/436 It is the ninth edition of this "traditional'' meeting in Pisa, after the ones in 2001, 2003, 2006, 2008, 2010, 2012, 2014 and 2016. Organizing Committee Luigi Ambrosio, Scuola Normale Superiore, Pisa Giuseppe Buttazzo, Dipartimento di Matematica, UniversitĂ 

From playlist Centro di Ricerca Matematica Ennio De Giorgi

Video thumbnail

09 Implicit Function Theorem

We introduce the implicit function theorem ansatz, as a way for solving optimization problems with equality constraints.

From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)

Video thumbnail

Kate Warne: America's First Female Detective and the Pinkerton Agency

When Allan Pinkerton started his famed Pinkerton Detective Agency, he hired Kate Warne as a female detective. Among her many accomplishments, some of which have been lost to history, she helped foil a plot to assassinate then-President elect Abraham Lincoln. America's first female detectiv

From playlist Wild West

Video thumbnail

Tested in 2016: Kishore Hari's Favorite Things!

Our science lead Kishore shares his favorite things of 2016! Unsurprisingly, his list is filled with some science-themed recommendations, but Kishore also has a few book picks and one piece of technology that's changed his home life. Little Passports Science Expeditions 17.95 per month h

From playlist Staff Favorites

Video thumbnail

The Definition of the Derivative

An introduction / explanation of the definition of the derivative. Make sure to check out the 3Blue1Brown video: https://www.youtube.com/watch?v=9vKqVkMQHKk Keep flexin' those brain muscles! Facebook: https://www.facebook.com/braingainzofficial Instagram: https://www.instagram.com

From playlist Calculus I

Video thumbnail

Claire Amiot: Cluster algebras and categorification - Part 3

Abstract: In this course I will first introduce cluster algebras associated with a triangulated surface. I will then focus on representation of quivers, and show the strong link between cluster combinatorics and representation theory. The aim will be to explain additive categorification of

From playlist Combinatorics

Video thumbnail

Calculus 3.03a - The Derived Function

The Derived Function, or better known as simply The Derivative. This is the beginning of the material on the definition of the derivative. The topic is approached in a fairly standard manner as the general case of the limit of a difference quotient.

From playlist Calculus Ch 3 - Derivatives

Video thumbnail

Lecture 0 - Course Administration

This is Lecture 0 of the CSE519 (Data Science) course taught by Professor Steven Skiena [http://www.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: http://www.cs.stonybrook.edu/~skiena/519 More information may be found here: http://www.

From playlist CSE519 - Data Science Fall 2016

Video thumbnail

Derivative Of A Square Root!! (Calculus)

#Math #Calculus #Physics #Tiktok #Studyhacks #NicholasGKK #Shorts

From playlist Calculus

Video thumbnail

The Unified Transform Method for linear evolution equations (Lecture 2) by David Smith

Program : Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

Related pages

One-sided limit | Real analysis | Differentiable function | Ulisse Dini | Extended real number line | Mathematics | Vector space | Lipschitz continuity | Derivative | Continuous function