Smooth functions | Calculus of variations | Lemmas in analysis
In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point.Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic versions are easy to formulate and prove. More powerful versions are used when needed. (Wikipedia).
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
Statement of Calculus of Variations (6.1)
In this video, I state the calculus of variations problem, and describe how to solve it.
From playlist Intermediate Classical Mechanics
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Calculus 5.3 The Fundamental Theorem of Calculus
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
Calculus: The Fundamental Theorem of Calculus
This is the second of two videos discussing Section 5.3 from Briggs/Cochran Calculus. In this section, I discuss both parts of the Fundamental Theorem of Calculus. I briefly discuss why the theorem is true, and work through several examples applying the theorem.
From playlist Calculus
Calculus - The Fundamental Theorem, Part 3
The Fundamental Theorem of Calculus. Specific examples of simple functions, and how the antiderivative of these functions relates to the area under the graph.
From playlist Calculus - The Fundamental Theorem of Calculus
Extended Fundamental Theorem of Calculus
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Extended Fundamental Theorem of Calculus. You can use this instead of the First Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus. - Formula - Proof sketch of the formula - Six Examples
From playlist Calculus
Ex 1: The Second Fundamental Theorem of Calculus
This video provides an example of how to apply the second fundamental theorem of calculus to determine the derivative of an integral. Site:http://mathispower4u.com
From playlist The Second Fundamental Theorem of Calculus
8ECM Plenary Lecture: Franc Forstnerič
From playlist 8ECM Plenary Lectures
John Harrison - Formalization and Automated Reasoning: A Personal and Historical Perspective
Recorded 13 February 2023. John Harrison of Amazon Web Services presents "Formalization and Automated Reasoning: A Personal and Historical Perspective" at IPAM's Machine Assisted Proofs Workshop. Abstract: In this talk I will try to first place the recent interest in machine-assisted proof
From playlist 2023 Machine Assisted Proofs Workshop
Joseph Miller: A derivation on the field of d.c.e.reals
Recording during the thematic meeting : "Computability, Randomness and Applications" the June 23, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's A
From playlist Logic and Foundations
Camillo De Lellis - Tribute to Ennio De Giorgi - 20 September 2016
De Lellis, Camillo "Min-max methods for surfaces with boundary"
From playlist A Mathematical Tribute to Ennio De Giorgi
Gronwall's inequality & fractional differential equations
Several general versions of Gronwall's inequality are presented and applied to fractional differential equations of arbitrary order. Applications include: yielding a priori bounds and nonumultiplicity of solutions. This presentation features new mathematical research. http://projecteucli
From playlist Mathematical analysis and applications
Ulrich Bauer (4/6/22): Persistence in functional topology
I will illustrate the central role and the historical development of persistent homology beyond applied topology, connecting recent developments in persistence theory with classical results in critical point theory and the calculus of variations. Presenting recent joint work with M. Schmah
From playlist AATRN 2022
Change of variables and the derivative -- Calculus I
This lecture is on Calculus I. It follows Part I of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus I
Karen Uhlenbeck: Some Thoughts on the Calculus of Variations
Abstract: I will talk about some of the classic problems in the calculus of variations, and describe some of the mathematics which was developed to solve them. We will begin with the Greeks and end with some of the tantalizing problems of today. This lecture was given by the 2019 Abel Lau
From playlist Karen K. Uhlenbeck
5 5 Ito s Rule, Ito s Lemma Part 1
BEM1105x Course Playlist - https://www.youtube.com/playlist?list=PL8_xPU5epJdfCxbRzxuchTfgOH1I2Ibht Produced in association with Caltech Academic Media Technologies. ©2020 California Institute of Technology
From playlist BEM1105x Course - Prof. Jakša Cvitanić
Math 031 012017 Calculus I review; Fundamental Theorem of Calculus (no sound)
(Sorry - someone kicked the microphone off, so there's no sound.) Calculus I review: Extreme Value Theorem, definition of derivative, rules of differentiation (linearity, product rule, quotient rule, Chain Rule), Mean Value Theorem, antiderivative, indefinite integral, definite integrals.
From playlist Course 3: Calculus II (Spring 2017)
De Giorgi–Nash–Moser and Hörmander theories: New interplays – Clément Mouhot – ICM2018
Mathematical Physics | Partial Differential Equations Invited Lecture 11.8 | 10.9 De Giorgi–Nash–Moser and Hörmander theories: New interplays Clément Mouhot Abstract: We report on recent results and a new line of research at the crossroad of two major theories in the analysis of partial
From playlist Partial Differential Equations