Theorems in complex analysis | Mathematical identities | E (mathematical constant) | Exponentials
In mathematics, Euler's identity (also known as Euler's equation) is the equality where e is Euler's number, the base of natural logarithms,i is the imaginary unit, which by definition satisfies i2 = −1, andπ is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for x = π. Euler's identity is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics. In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia).
This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com
From playlist Mathematics General Interest
Euler Pronunciation: In Depth Analysis
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From playlist Fun and Amazing Math
Euler's real identity NOT e to the i pi = -1
NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) I've got some good news and some bad news for you. The bad news is that Euler's identity e to the i pi =
From playlist Recent videos
In this video, I am going to be showing you how to derive Euler's Formula and Identity. #breakthroughjuniorchallenge #breakthroughjuniorchallenge2020 EXTRA TIDBITS OF INFORMATION: - There are a few applications of Euler's Identity. One important use of it is when calculating AC current i
From playlist Summer of Math Exposition Youtube Videos
Euler‘s identity e to the i pi = -1 and common sense
Euler's identity e to the i pi = -1 is a very general abstract algebraic identity. This video shows one concrete geometric realization of this famous equation starting from scratch. Can you find more? Using a line of thought expressed in Sir William Rowan Hamiltons "Elements of Quaternion
From playlist Summer of Math Exposition Youtube Videos
Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
Someone asked me a question about Euler's Identity (e^iπ = --1)...
...and despite it being almost entirely irrelevant to the lesson at hand, I couldn't resist spending 3 minutes talking about it because it's undiluted mathematical awesome.
From playlist Introduction to Complex Numbers
A (very) Brief History of Leonhard Euler
An incredibly brief history of Leonhard Euler! Not much math in this video, so just a heads up in the event you expect math-heavy. DISCORD ►► https://discord.gg/Jd3tCeK PATREON ►► https://www.patreon.com/moderndaymath
From playlist Mathematics named after Leonhard Euler
YOU CAN'T USE EULER'S IDENTITY TO PROVE THE ANGLE SUM IDENTITIES! | Tricky Parts of Calculus, Ep. 4
I give multiple proofs of the angle sum identities sin(x+y) = sin(x)cos(y) + sin(y)cos(x) and cos(x+y) = cos(x)cos(y) - sin(x)sin(y) from different perspectives. I stress that a very common presentation of these formulas based on Euler's identity e^(ix) = cos(x) + i sin(x) is circular and
From playlist Math
Are 3Blue1Brown and Khan Academy WRONG about Euler’s Formula? / [e to the i pi, e^(i*pi), beautiful]
Are 3Blue1Brown and Khan Academy WRONG about Euler’s Formula? [e to the i pi, e^(i*pi), beautiful] Euler's Identity as a special case of Euler's Formula: e^(i*pi)+1 = 0 (so e^(i*pi) = -1). So many people praise Euler's Identity as the most beautiful equation in all of mathematics, but d
From playlist Misc.
Marc Levine: Refined enumerative geometry (Lecture 2)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Lecture 2: Euler classes, Euler characteristics and Riemann-Hurwicz formulas The Euler class of a vector bundle is defined in the twisted Chow-Witt ring and gives rise to an Euler ch
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Tom Crawford shows us some cool things about Euler's Formula... Check https://brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓ Tom Crawford's website, with links to his work and other outreach:
From playlist Tom Crawford on Numberphile
Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab
In this video, we code up the Forward Euler and Backward Euler integration schemes in Python and Matlab, investigating stability and error as a function of the time step. We test these integrators on the simple spring-mass-damper system, where we have an analytic solution to compare again
From playlist Engineering Math: Differential Equations and Dynamical Systems
Power sum MASTER CLASS: How to sum quadrillions of powers ... by hand! (Euler-Maclaurin formula)
The longest Mathologer video ever! 50 minutes, will this work? Let's see before I get really serious about that Kurosawa length Galois theory video :) Today's video is another self-contained story of mathematical discovery covering millennia of math, starting from pretty much nothing and
From playlist Recent videos
Proof of Euler's Identity | Complex Numbers
Given any introduction to complex numbers, one sooner or later is exposed to Euler's formula (or Euler's identity), which expresses an exponential of an imaginary number in terms of the sum of two trigonometric functions. Many proofs are either technical or unenlightening and in most cases
From playlist Complex Analysis
Proving Euler's Formula (2 of 4: Differentiating both sides)
More resources available at www.misterwootube.com
From playlist Introduction to Complex Numbers
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 2/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory