Differential geometry of surfaces | Riemannian manifolds
In the mathematical field of differential geometry, the Simons formula (also known as the Simons identity, and in some variants as the Simons inequality) is a fundamental equation in the study of minimal submanifolds. It was discovered by James Simons in 1968. It can be viewed as a formula for the Laplacian of the second fundamental form of a Riemannian submanifold. It is often quoted and used in the less precise form of a formula or inequality for the Laplacian of the length of the second fundamental form. In the case of a hypersurface M of Euclidean space, the formula asserts that where, relative to a local choice of unit normal vector field, h is the second fundamental form, H is the mean curvature, and h2 is the symmetric 2-tensor on M given by h2ij = gpqhiphqj.This has the consequence that where A is the shape operator. In this setting, the derivation is particularly simple: the only tools involved are the Codazzi equation (equalities #2 and 4), the Gauss equation (equality #4), and the commutation identity for covariant differentiation (equality #3). The more general case of a hypersurface in a Riemannian manifold requires additional terms to do with the Riemann curvature tensor. In the even more general setting of arbitrary codimension, the formula involves a complicated polynomial in the second fundamental form. (Wikipedia).
Binet's formula | Lecture 5 | Fibonacci Numbers and the Golden Ratio
Derivation of Binet's formula, which is a closed form solution for the Fibonacci numbers. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confir
From playlist Fibonacci Numbers and the Golden Ratio
Computing the Sums of Finite Series with Formulas
Computing the Sums of Finite Series with Formulas. Several examples where we use formulas to compute the sums. Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The formulas are as follows, with all sums starting at i = 1. sum(c) = nc sum(i) = n(n + 1)/2 sum(i^2) = n(n + 1)(2n +
From playlist Precalculus and Algebra
Amazing Pi Formula - Prime Numbers and Multiples of 4
Tom Rocks Maths intern Isaac Wood introduces the most amazing formula for pi - involving prime numbers and multiples of 4 - and shows you how to prove it. The proof is broken down into several steps. We begin by proving 'Mini Result 1' which gives the sum of an infinite geometric series.
From playlist Mathstars
AMAZING Formula For Pi (π) - The Wallis Product
Start with the pair of fractions (2/1)(2/3). Now increment each number by 2 to get the pair of fractions (4/3)(4/5). Repeat this to get the next pair, and repeat this infinitely many times. If you then multiply all the fractions, you get a marvelous value: it is equal to pi divided by 2. T
From playlist Pi
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
Dimitri Zvonkine - On two ELSV formulas
The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class
From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves
Second Order Recurrence Formula (1 of 3: Prologue - considering the old course)
More resources available at www.misterwootube.com
From playlist Further Proof by Mathematical Induction
This video show how to use the distance formula to determine the distance between two points. It also shows how it is derived from the Pythagorean theorem. http://mathispower4u.yolasite.com/
From playlist Using the Distance Formula / Midpoint Formula
How to Find the Distance Between Two Points - How to Use the Distance Formula
This tutorial shows how the distance formula is used to find the distance between two points in a x y coordinate system. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)
From playlist Pythagorean Theorem and the Distance Formula
Excel - Random Walk Down Wall Street - Podcast 2035
Microsoft Excel - Random Walk Down Wall Street. Creating a what-if Data Table from a blank cell if your model includes RAND. Episode Recap: Today's trick is from Professor Simon Benninga Game of penny-pitching. 50/50 chance that player A or player B doubles their money Play 25 rounds of pe
From playlist Full Advanced Excel Course - Free
2020 Theory Winter School: Srinivas Raghu (pt2)
Topic: Boson-ferimon duality in strongly coupled field theories Part 2 For more information on the 2020 Theory Winter School: https://nationalmaglab.org/news-events/events/for-scientists/winter-theory-school
From playlist 2020 Theory Winter School
Developments in 4-manifold topology arising from a theorem of Donaldson's - John Morgan [2017]
slides for this talk: https://drive.google.com/file/d/1_wHviPab9klzwE4UkCOvVecyopxDsZA3/view?usp=sharing Name: John Morgan Event: Workshop: Geometry of Manifolds Event URL: view webpage Title: Developments in 4-manifold topology arising from a theorem of Donaldson's Date: 2017-10-23 @9:3
From playlist Mathematics
Transcendental Numbers - Numberphile
Numbers like e and Pi cannot be made using normal algebra. Featuring Australia's Numeracy Ambassador, Simon Pampena. Extra footage: http://youtu.be/dzerDfN2E7U More links & stuff in full description below ↓↓↓ Discussing transendental numbers, algebraic numbers, pi, e and other stuff. S
From playlist Numberphile Videos
Lecture 11-Jack Simons Electronic Structure Theory- Density functional theory
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From playlist U of Utah: Jack Simons' Electronic Structure Theory course
Spenta Wadia - Fermion-Boson Duality in 2+1 dim. large N Gauge Theories (1)
PROGRAM: THE 8TH ASIAN WINTER SCHOOL ON STRINGS, PARTICLES AND COSMOLOGY DATES: Thursday 09 Jan, 2014 - Saturday 18 Jan, 2014 VENUE: Blue Lily Hotel, Puri PROGRAM LINK: http://www.icts.res.in/program/asian8 The 8th Asian Winter School on Strings, Particles and Cosmology is part of a seri
From playlist The 8th Asian Winter School on Strings, Particles and Cosmology
Regularity of stable codimension 1 CMC varifolds - Neshan Wickramasekera
Variational Methods in Geometry Seminar Topic: Regularity of stable codimension 1 CMC varifolds Speaker: Neshan Wickramasekera Affiliation: University of Cambridge; Member, School of Mathematics Date: January 15, 2019 For more video please visit http://video.ias.edu
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OSCON 2010: Mark Masterson, "Is the Enterprise Ready for the Cloud?"
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From playlist OSCON 10 Cloud Summit
De Moivre's formula: a COOL proof
A quick way of proving De Moivre's formula! Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook Hi again everyone, Chris Tisdell here again. In this presentation I am going to continue my series of videos on complex numbers. In particular, in this presentation, I am g
From playlist Intro to Complex Numbers
Lecture 12-Jack Simons Electronic Structure Theory- Gradients and reaction paths
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From playlist U of Utah: Jack Simons' Electronic Structure Theory course