Convex analysis | Variational principles | Theorems in functional analysis | Variational analysis
In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. Ekeland's principle can be used when the lower level set of a minimization problems is not compact, so that the Bolzano–Weierstrass theorem cannot be applied. The principle relies on the completeness of the metric space. The principle has been shown to be equivalent to completeness of metric spaces.In proof theory, it is equivalent to Π11CA0 over RCA0, i.e. relatively strong. It also leads to a quick proof of the Caristi fixed point theorem. (Wikipedia).
Variational Principle Introduction
In this video, I introduce the variational principle in quantum mechanics, how it is derived, and why you might want to use it. Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos. This
From playlist Quantum Mechanics
Paul Shafer:Reverse mathematics of Caristi's fixed point theorem and Ekeland's variational principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Caristi's fixed point theorem is a fixed point theorem for functions that are controlled by continuous functions but are necessarily continuous themselves. Let a 'Caristi
From playlist Workshop: "Proofs and Computation"
Free ebook http://tinyurl.com/EngMathYT I show how to solve differential equations by applying the method of variation of parameters for those wanting to review their understanding.
From playlist Differential equations
Introduction to Direct Variation, Inverse Variation, and Joint Variation
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Direct Variation, Inverse Variation, and Joint Variation
From playlist 3.7 Modeling Using Variation
Ivar Ekeland a été interviewé par le CIRM (Centre International de Rencontres Mathématiques) lors des Journées Nationales de l’APMEP organisées du 19 au 22 octobre 2013. Ivar Ekeland, invité par les Sociétés savantes, a donné une conférence sur les mathématiques de la planète Terre, "Le t
From playlist Math of Planet Earth
Variation of Parameters for Systems of Differential Equations
This is the second part of the variation of parameters-extravaganza! In this video, I show you how to use the same method in the last video to solve inhomogeneous systems of differential equations. Witness how linear algebra makes this method so elegant!
From playlist Differential equations
Here I go over an example of using the variational principle to find an upper bound on the ground state energy of a neat potential - the infinite triangular well. Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestion
From playlist Quantum Mechanics
Differential Equations | Variation of Parameters.
We derive the general form for a solution to a differential equation using variation of parameters. http://www.michael-penn.net
From playlist Differential Equations
Variation of Constants / Parameters
Download the free PDF http://tinyurl.com/EngMathYT A basic illustration of how to apply the variation of constants / parameters method to solve second order differential equations.
From playlist Differential equations
Minyi Huang: "Mean field Stackelberg Games: State Feedback Equilibrium"
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From playlist High Dimensional Hamilton-Jacobi PDEs 2020
A16 The method of variation of parameters
Starting the derivation for the equation that is used to find the particular solution of a set of differential equations by means of the variation of parameters.
From playlist A Second Course in Differential Equations
C29 Variation of parameters Part 2
I continue with an explanation of the method of variation of parameters.
From playlist Differential Equations
Noether's theorems and their growing physical relevance by Joseph Samuel
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether
Univers Convergents 2016 - séance 1/6 - "A Beautiful Mind"
A Beautiful Mind de Ron Howard (USA - 2001 - 2h15) avec Russell Crowe, Ed Harris, Jennifer Connelly Mardi 26 janvier 2016 - 19h30 John Forbes Nash Jr (1928-2015) est un des plus grands génies mathématiques du XXème siècle. Chercheur surdoué, il est le père d’une « théorie économiq
From playlist Ciné-Club Univers Convergents
06: Hamilton´s principles - Part 2
Jacob Linder: 18.01.2012, Classical Mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics
Lec 7 | MIT 3.320 Atomistic Computer Modeling of Materials
Technical Aspects of Density Functional Theory View the complete course at: http://ocw.mit.edu/3-320S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.320 Atomistic Computer Modeling of Materials
13. The Einstein field equation (variant derivation).
MIT 8.962 General Relativity, Spring 2020 Instructor: Scott Hughes View the complete course: https://ocw.mit.edu/8-962S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx A second route to the Einstein field equation, using a variational principle
From playlist MIT 8.962 General Relativity, Spring 2020
Pavel Zorin-Kranich: Variational and jump inequalities
Abstract: Variational norms are parametrization-invariant versions of Hölder norms. They appear in the theory of rough paths and can also be used to quantify various convergence results, e.g. for truncated singular integrals and ergodic averages. Endpoint versions of such quantified result
From playlist Follow-up Workshop to TP "Harmonic Analysis and Partial Differential Equations"
Your Daily Equation #19 : At the Core of Fundamental Physics: The Principle of Least Action
Episode 19 #YourDailyEquation: All fundamental laws of physics share a reliance on a single principle: The Principle of Least Action. In this episode of Your Daily Equation, Brian Greene explains this principle in the simplest example and shows how it yields the basic laws of motion introd
From playlist Your Daily Equation with Brian Greene