Differential geometry of surfaces | Theorems in differential geometry
In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions in which the surface curves the most and the least. The theorem is named for Leonhard Euler who proved the theorem in. More precisely, let M be a surface in three-dimensional Euclidean space, and p a point on M. A normal plane through p is a plane passing through the point p containing the normal vector to M. Through each (unit) tangent vector to M at p, there passes a normal plane PX which cuts out a curve in M. That curve has a certain curvature κX when regarded as a curve inside PX. Provided not all κX are equal, there is some unit vector X1 for which k1 = κX1 is as large as possible, and another unit vector X2 for which k2 = κX2 is as small as possible. Euler's theorem asserts that X1 and X2 are perpendicular and that, moreover, if X is any vector making an angle θ with X1, then The quantities k1 and k2 are called the principal curvatures, and X1 and X2 are the corresponding principal directions. Equation is sometimes called Euler's equation . (Wikipedia).
Differential Equations | Euler's Method
We derive Euler's method for approximating solutions to first order differential equations.
From playlist Mathematics named after Leonhard Euler
Euler’s method - How to use it?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,
From playlist Differential Equations
Differential Equations | The solution of a Cauchy-Euler Differential Equation
We prove a general theorem regarding the form of a solution of a Cauchy-Euler Differential Equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Mathematics named after Leonhard Euler
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
How to derive Euler's formula using differential equations! Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook A somewhat new proof for the famous formula of Euler. Here is the famous formula named after the mathematician Euler. It relates the exponential with cosin
From playlist Intro to Complex Numbers
Solves the Euler differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equations-engineers Vector Calculus for Engineers: htt
From playlist Differential Equations
Differential Equations | Euler Equations Example 2
We solve a second order differential equation known as an Euler equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Differential Equations
Gianmarco Vega-Molino (U Conn) -- Heat Kernel Approach to Index Theorem
We discuss the application of heat kernel approximations to the proof of index theorems on Riemannian manifolds.
From playlist Northeastern Probability Seminar 2020
Differential Equations | Euler Equations Example 3
We solve a second order differential equation known as an Euler equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Differential Equations
Dynamics, numerical analysis and some geometry – Christian Lubich – ICM2018
Plenary Lecture 18 Dynamics, numerical analysis and some geometry Christian Lubich Abstract: Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we revi
From playlist Plenary Lectures
Looking at Euler flows through a contact mirror: Universality, Turing… - Eva Miranda
Workshop on the h-principle and beyond Topic: Looking at Euler flows through a contact mirror: Universality, Turing completeness and undecidability Speaker: Eva Miranda Affiliation: Universitat Politècnica de Catalunya Date: November 1, 2021 The dynamics of an inviscid and incompressible
From playlist Mathematics
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
Machine- Learning the Landscape (Lecture 1) by Yang-Hui He
PROGRAM KAVLI ASIAN WINTER SCHOOL (KAWS) ON STRINGS, PARTICLES AND COSMOLOGY (ONLINE) ORGANIZERS Francesco Benini (SISSA, Italy), Bartek Czech (Tsinghua University, China), Dongmin Gang (Seoul National University, South Korea), Sungjay Lee (Korea Institute for Advanced Study, South Korea
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (ONLINE) - 2022
Hausdorff School: Lecture by László Székelyhidi
Inauguration of the Hausdorff School The “Hausdorff School for Advanced Studies in Mathematics” is an innovative new program for postdocs by the Hausdorff Center. The official inauguration took place on October 20, 2015. Lecture by László Székelyhidi on "The h-principle in fluid mechanic
From playlist Inauguration of Hausdorff School 2015
Eckhard Meinrenken: Differential Geometry of Weightings
Talk by Eckhard Meinrenken in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/differential_geometry_of_weightings/ on February 19, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Camillo De Lellis: The Onsager Theorem
Abstract: In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. Ten
From playlist Mathematical Physics
Maps between Surfaces by Athanase Papadopoulos
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Lecture 15: Curvature of Surfaces (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
C36 Example problem solving a Cauchy Euler equation
An example problem of a homogeneous, Cauchy-Euler equation, with constant coefficients.
From playlist Differential Equations