Theorems in analysis | Numerical differential equations
In numerical analysis, the Lax equivalence theorem is a fundamental theorem in the analysis of finite difference methods for the numerical solution of partial differential equations. It states that for a consistent finite difference method for a well-posed linear initial value problem, the method is convergent if and only if it is stable. The importance of the theorem is that while the convergence of the solution of the finite difference method to the solution of the partial differential equation is what is desired, it is ordinarily difficult to establish because the numerical method is defined by a recurrence relation while the differential equation involves a differentiable function. However, consistency—the requirement that the finite difference method approximates the correct partial differential equation—is straightforward to verify, and stability is typically much easier to show than convergence (and would be needed in any event to show that round-off error will not destroy the computation). Hence convergence is usually shown via the Lax equivalence theorem. Stability in this context means that a matrix norm of the matrix used in the iteration is at most unity, called (practical) Lax–Richtmyer stability. Often a von Neumann stability analysis is substituted for convenience, although von Neumann stability only implies Lax–Richtmyer stability in certain cases. This theorem is due to Peter Lax. It is sometimes called the Lax–Richtmyer theorem, after Peter Lax and Robert D. Richtmyer. (Wikipedia).
Univalent foundations and the equivalence principle - Benedikt Ahrens
Short Talks by Postdoctoral Members Benedikt Ahrens - September 21, 2015 http://www.math.ias.edu/calendar/event/88134/1442858400/1442859300 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
Put all three properties of binary relations together and you have an equivalence relation.
From playlist Abstract algebra
Equivalence Relations Definition and Examples
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.
From playlist Abstract Algebra
Equivalence Relation on a Group Two Proofs
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relation on a Group Two Proofs. Given a group G and a subgroup H of G, we prove that the relation x=y if xy^{-1} is in H is an equivalence relation on G. Then cosets are defined and we prove that s_1 = s_2 iff [s_1] = [s
From playlist Abstract Algebra
What is Einstein's Equivalence Principle?
To check out the physics courses that I mentioned (many of which are free!) and to support this channel, go to https://brilliant.org/Sabine/ and create your Brilliant account. The first 200 will get 20% off the annual premium subscription. In this video I explain what the equivalence prin
From playlist Physics
Discrete Math - 9.5.1 Equivalence Relations
Exploring a special kind of relation, called an equivalence relation. Equivalence classes and partitions are also discussed. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
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Fundamentals of Mathematics - Lecture 26: Well-Definedness
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From playlist Fundamentals of Mathematics
Title: Rational Matrix Differential Operators and Integral Systems of PDEs
From playlist Fall 2017
Peter Lax: Abstract Phragmen-Lindelöf theorem & Saint Venant’s principle
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From playlist Abel Lectures
Angélica M. Osorno : (2)-categorical constructions and multiplicative equivariant Barratt (...)
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Peter Lax - The Abel Prize Interview 2005
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Radek Adamczak: Functional inequalities and concentration of measure II
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From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
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From playlist Hydrodynamics and fluctuations - microscopic approaches in condensed matter systems (ONLINE) 2021
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From playlist Abstract algebra
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Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn The Equivalence Principle in 3 examples: 1) The observers can not tell the difference of playing volleyball on Earth or
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Lec 4 | MIT 18.086 Mathematical Methods for Engineers II
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From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06
This video is one of the cornerstones of our dual space extravaganza. Using just some facts about annihilators (in a video below), I provide a very elegant and neat proof of the fact that the rank of A^T equals to the rank of A. Annihilator: https://www.youtube.com/watch?v=ISs13W6474g Cl
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This video covers the laws of limits and how we use them to evaluate a limit. These laws are especially handy for continuous functions. More theorems about limits are introduced in later videos. For more videos visit http://www.mysecretmathtutor.com
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