Differential equations | Calculus of variations | Differential geometry
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largelyto the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck, Clifford Taubes, Shing-Tung Yau, Richard Schoen, and Richard Hamilton launched a particularly exciting and productive era of geometric analysis that continues to this day. A celebrated achievement was the solution to the Poincaré conjecture by Grigori Perelman, completing a program initiated and largely carried out by Richard Hamilton. (Wikipedia).
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
An introduction to the idea of Dimensional Analysis
From playlist Mathematical Physics I Uploads
Geometric Algebra - Linear Transformations, Outermorphism, and the Determinant
In this video, we will review some basic concepts from linear algebra, such as the linear transformation, prove important theorems which ground matrix operations, extend the linear transformation on vectors to higher-graded elements to bivectors and trivectors, and define the determinant o
From playlist Geometric Algebra
Geometric Algebra - The Matrix Representation of a Linear Transformation
In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.
From playlist Geometric Algebra
What is the definition of a geometric sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
How to determine the altitude by using the geometric mean
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Using the geometric mean to determine the missing parts of a triangle
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Geometric Algebra, First Course, Episode 08: The Geometric Product.
We finally arrive at the ability to multiply our Geometric numbers together. We see where the geometric product comes from, leading to the definition for vector multiplication, and we add some definitions that allow us to multiply all elements of our algebra. We also use automated testing
From playlist Geometric Algebra, First Course, in STEMCstudio
Quasi-periodic solutions to nonlinear PDE's - Wei-Min Wang
Analysis Seminar Topic: Quasi-periodic solutions to nonlinear PDE's Speaker:Wei-Min Wang Affiliation: Université Paris-Sud Date: October 26, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Rasch measurement using user-friendly jMetrik | Powerful free software
jMetrik is a free, user-friendly, and open source psychometric software which runs on any Windows, Mac OSX, or Linux platforms that have a current version of Java. In this video, I demonstrate how to run a Rasch measurement on binary data and compare the output with Winsteps. There is sign
From playlist Item response theory
Geometric Algebra 19 3D Geometric Algebra
In this lesson we examine the 3D geometric algebra for the Euclidean case. This is simpler than the spacetime algebra we have been considering so far. First, we construct the basis for the 3D algebra and then begin to make contact with the standard vector algebra of elementary physics. Aft
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 13 Tensors
In this lesson we make contact with the standard concept of tensors using spacetime algebra. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually use to produce the lectures is: https://apps.apple.com/us/app/vittle-pro-video-whit
From playlist QED- Prerequisite Topics
James Arthur: The Langlands program: arithmetic, geometry and analysis
Abstract: As the Abel Prize citation points out, the Langlands program represents a grand unified theory of mathematics. We shall try to explain in elementary terms what this means. We shall describe an age old question concerning the arithmetic prime numbers, together with a profound gene
From playlist Abel Lectures
Convergent Evolving Surface Finite Element Algorithms for Geometric Evolution Equations
Professor Christian Lubich University of Tübingen, Germany
From playlist Distinguished Visitors Lecture Series
QED Prerequisites Geometric Algebra: Introduction and Motivation
This lesson is the beginning of a significant diversion from QED prerequisites. No student needs to understand Geometric Algebra in order to begin the study of QED. However, since we have pushed the formal structure of Maxwell's Equations as far as I know how to go, I think it makes sense
From playlist QED- Prerequisite Topics
SIGGRAPH 2022 - Geometric Algebra
The SIGGRAPH 2022 course on Geometric Algebra. by Alyn Rockwood and Dietmar Hildenbrand
From playlist Introductory
Lecture 13 - Financial Time Series Data
This is Lecture 13 of the COMP510 (Computational Finance) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Hong Kong University of Science and Technology in 2008. The lecture slides are available at: http://www.algorithm.cs.sunysb.edu/computationalfinance/pd
From playlist COMP510 - Computational Finance - 2007 HKUST
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Abel Award Ceremony 2019 - Karen Uhlenbeck
The Abel Prize Award Ceremony, May 21, 2019. Place: The University Aula, Oslo, Norway Programme: 0:08 Procession accompanied by the “Abel Fanfare” (Klaus Sandvik). Performed by musicians from The Staff Band of the Norwegian Armed Forces 1:00 His Majesty King Harald V enters the University
From playlist Karen K. Uhlenbeck