Infinity | Field (mathematics)
In mathematics, the Levi-Civita field, named after Tullio Levi-Civita, is a non-Archimedean ordered field; i.e., a system of numbers containing infinite and infinitesimal quantities. Each member can be constructed as a formal series of the form where are real numbers, is the set of rational numbers, and is to be interpreted as a positive infinitesimal. The support of , i.e., the set of indices of the nonvanishing coefficients must be a left-finite set: for any member of , there are only finitely many members of the set less than it; this restriction is necessary in order to make multiplication and division well defined and unique. The ordering is defined according to the dictionary ordering of the list of coefficients, which is equivalent to the assumption that is an infinitesimal. The real numbers are embedded in this field as series in which all of the coefficients vanish except . (Wikipedia).
A Ridiculously Huge Pair of Ancient Galaxies
To support SciShow Space and learn more about Brilliant, go to https://brilliant.org/scishowspace/ Astronomers have found a couple galaxies that were much larger than expected, and the Opportunity rover might be in for some harsh Martian weather! We want to learn more about you and your
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The Biggest Volcano in the Solar System
Get to know Olympus Mons on Mars, the biggest volcano in the solar system, and find out why a planet that’s smaller than Earth has volcanoes that are bigger than ours! Hosted by: Hank Green ---------- Dooblydoo thanks to the following Patreon supporters -- we couldn't make SciShow without
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04: D´Alembert´s principle part 2
Jacob Linder: Lecture 2, 11.01.2012, Klassisk Mekanikk (TFY 4345) 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
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There's a Giant Hole in the Universe
There’s basically a hole in the universe -- a region where there’s much less matter than there should be. And we don’t know why it’s there. Hosted by: Caitlin Hofmeister ---------- Dooblydoo thanks to the following Patreon supporters -- we couldn't make SciShow without them! Shout outs go
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Divergence of the cross product of two vectors (proof) | Lecture 22 | Vector Calculus for Engineers
An example of how to prove a vector calculus identity using the Levi-Civita symbol and the Kronecker delta. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Subscribe to my ch
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Vector Identities | Lecture 8 | Vector Calculus for Engineers
Four vector identities are presented: (1) Scalar triple product; (2) Vector triple product; (3) Scalar quadruple product; (4) Vector quadruple product. The tools required to prove them are discussed. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture n
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The Oldest Crater from a Meteorite…Isn’t a Crater after All?
There's one crater that may be older than any that we know of. Except there's a snag, it might not actually be a crater at all. Hosted By: Hank Green SciShow is on TikTok! Check us out at https://www.tiktok.com/@scishow ---------- Support SciShow Space by becoming a patron on Patreon: h
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Levi-Civita and Kronecker: A Remarkable Relationship | Deep Dive Maths
There is a remarkable relationship between the product of two Levi-Civita symbols and the determinant of a matrix with the Kronecker delta as elements. After defining the Levi-Civita symbol and the Kronecker delta, I show how to derive this relationship using permutation matrices and the
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The Massive Chunk of Metal Hiding in the Moon
The moon's South Pole-Aitken basin is the largest known crater in existence, and there's something big hidden underneath. Hosted By: Reid Reimers SciShow is on TikTok! Check us out at https://www.tiktok.com/@scishow ---------- Support SciShow Space by becoming a patron on Patreon: https
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Kronecker delta and Levi-Civita symbol | Lecture 7 | Vector Calculus for Engineers
Definition of the Kronecker delta and the Levi-Civita symbol (sometimes called the permutation symbol or Levi-Civita tensor). The relationship between the Kronecker delta and the Levi-Civita symbol is discussed. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engin
From playlist Vector Calculus for Engineers
Vector Triple Product | Lecture 10 | Vector Calculus for Engineers
The vector triple product identity is proved using the Levi-Civita symbol and the Einstein summation convention. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Subscribe to
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An Oxford Mathematics Graduate Supervision - Geometry and Physics in 7 Dimensions
So how do supervisor & graduate student work together? What happens in a graduate supervision? To find out, we filmed a supervision. Introducing Professor Jason Lotay & graduate student Izar Alonso Lorenzo as they discuss geometry in seven dimensions related to special holonomy, gauge the
From playlist Oxford Mathematics Student Tutorials and Graduate Supervisions
Tensor Calculus Lecture 7c: The Levi-Civita Tensors
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Hayabusa: The Artificial Meteor Launched From An Asteroid
After we retrieved samples of the moon, it was quite a while before we could land on anything else and bring bits of it back home. Hosted By: Reid Reimers ---------- Huge thanks go to the following Patreon supporter for helping us keep SciShow Space free for everyone forever: Jason A Sasl
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Nuclear Pasta May Be the Strongest Material Ever | SciShow News
There is some super weird, noodley stuff inside neutron stars and scientists have found evidence that black holes can have strange geometries. For special, curated artifacts of this universe, check out https://scishowfinds.com/ ---------- Support SciShow by becoming a patron on Patreon: h
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The Strongest Magnetic Field in the Universe
Hint: It's not your collection of awesome refrigerator magnets! ---------- Support SciShow by becoming a patron on Patreon: https://www.patreon.com/scishow ---------- Dooblydoo thanks go to the following Patreon supporters—we couldn't make SciShow without them! Shoutout to Kevin Bealer, M
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There's an Interstellar Asteroid Hiding Near Jupiter
We may have found another interstellar asteroid and scientists have some new ideas about how Saturn's moons got their weird shapes. Host: Hank Green For special, curated artifacts of this universe, check out https://scishowfinds.com/ ---------- Support SciShow by becoming a patron on Pat
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http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Tensor Calculus Change of Coordinates The Tensor Desc
From playlist Introduction to Tensor Calculus
Tensor Calculus Lecture 10a: The Covariant Surface Derivative in Its Full Generality
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Stardust Discovery, and 2 Planetary Conjunctions
SciShow Space shares the latest developments from around the universe, including news about the first material ever collected from outside the solar system, and a backyard astronomers’ guide to two upcoming planetary conjunctions. Hosted by: Reid Reimers ---------- Like SciShow? Want to h
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