In mathematics, an incompressible surface is a surface properly embedded in a 3-manifold, which, in intuitive terms, is a "nontrivial" surface that cannot be simplified. In non-mathematical terms, the surface of a suitcase is compressible, because we could cut the handle and shrink it into the surface. But a Conway sphere (a sphere with four holes) is incompressible, because there are essential parts of a knot or link both inside and out, so there is no way to move the entire knot or link to one side of the punctured sphere. The mathematical definition is as follows. There are two cases to consider. A sphere is incompressible if both inside and outside the sphere there are some obstructions that prevent the sphere from shrinking to a point and also prevent the sphere from expanding to encompass all of space. A surface other than a sphere is incompressible if any disk with its boundary on the surface spans a disk in the surface. Incompressible surfaces are used for decomposition of Haken manifolds, in normal surface theory, and in the study of the fundamental groups of 3-manifolds. (Wikipedia).
This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
MATH331: Riemann Surfaces - part 1
We define what a Riemann Surface is. We show that PP^1 is a Riemann surface an then interpret our crazy looking conditions from a previous video about "holomorphicity at infinity" as coming from the definition of a Riemann Surface.
From playlist The Riemann Sphere
Introduction to Quadric Surfaces
http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between convex and concave
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Complex surfaces 2: Minimal surfaces
This talk is part of a series about complex surfaces, and explains what minimal surfaces are. A minimial surfaces is one that cannot be obtained by blowing up a nonsingular surfaces at a point. We explain why every surface is birational to a minimal nonsingular projective surface. We disc
From playlist Algebraic geometry: extra topics
Multivariable Calculus | The tangent plane of a level surface.
We derive the equation of a plane tangent to a level surface. That is, a surface defined by the equation F(x,y,z)=k. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Quadric Surface: The Ellipsoid
This video explains how to determine the traces of an ellipsoid and how to graph an ellipsoid. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
The Continuity Equation: A PDE for Mass Conservation, from Gauss's Divergence Theorem
This video dives into Gauss's Divergence theorem to derive the partial differential equation (PDE) for mass conservation, known as the continuity equation. This is one of the most fundamental equations in fluid mechanics. Specifically, for incompressible flows, the mass continuity equati
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
Jayanta Bhattacharjee - Introduction to fluid dynamics and turbulence (2)
PROGRAM: BANGALORE SCHOOL ON STATISTICAL PHYSICS - V DATES: Monday 31 Mar, 2014 - Saturday 12 Apr, 2014 VENUE: Raman Research Institute, Bangalore PROGRAM LINK: http://www.icts.res.in/program/BSSP2014 This advanced level school was started in 2010 at the Raman Research Institute, Banga
From playlist Bangalore School on Statistical Physics - V
Conservation of Mass, part 4 - Lecture 2.4 - Chemical Engineering Fluid Mechanics
Integral form of the conservation of mass. This video is part of a series of screencast lectures presenting content from an undergraduate-level fluid mechanics course in the Artie McFerrin Department of Chemical Engineering at Texas A&M University (College Station, TX, USA). The screenc
From playlist TAMU: Fluid Mechanics in Chemical Engineering with Prof. Victor Ugaz | CosmoLearning.org ChemE
John Pardon: Totally disconnected groups (not) acting on three-manifolds
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Geometry
Smoothing finite group actions on three-manifolds – John Pardon – ICM2018
Topology Invited Lecture 6.13 Smoothing finite group actions on three-manifolds John Pardon Abstract: There exist continuous finite group actions on three-manifolds which are not smoothable, in the sense that they are not smooth with respect to any smooth structure. For example, Bing co
From playlist Topology
Potential Flow Part 2: Details and Examples
This video gives more examples of potential flows and how they establish idealized fluid flows. They are found by solving Laplace's equation, which is one of the most important PDEs in all of mathematical physics. @eigensteve on Twitter eigensteve.com databookuw.com %%% CHAPTERS %
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
mod-04 lec-04 Incompressible Fluid Flow related to Fluid Drive
Fundamentals of Industrial Oil Hydraulics and Pneumatics by Prof. R.N. Maiti,Department of Mechanical Engineering,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Fundamentals of Industrial Oil Hydraulics and Pneumatics (CosmoLearning Mechanical Engineering)
Jintian Zhu - Incompressible hypersurface, positive scalar curvature and positive mass theorem
In this talk, I will introduce a positive mass theorem for asymptotically flat manifolds with fibers (like ALF and ALG manifolds) under an additional but necessary incompressible condition. I will also make a discussion on its connection with surgery theory as well as quasi-local mass and
From playlist Not Only Scalar Curvature Seminar
Derivation of the energy equation
Video lectures for Transport Phenomena course at Olin College. This video derives the conservation of energy equation for an incompressible, Newtonian flow.
From playlist Lectures for Transport Phenomena course
11_6_1 Contours and Tangents to Contours Part 1
A contour is simply the intersection of the curve of a function and a plane or hyperplane at a specific level. The gradient of the original function is a vector perpendicular to the tangent of the contour at a point on the contour.
From playlist Advanced Calculus / Multivariable Calculus
Yao Yao: "Small scale formations in the incompressible porous media equation"
Transport and Mixing in Complex and Turbulent Flows 2021 "Small scale formations in the incompressible porous media equation" Yao Yao - Georgia Institute of Technology Abstract: The incompressible porous media (IPM) equation is an active scalar equation where the density is transported b
From playlist Transport and Mixing in Complex and Turbulent Flows 2021
What are four types of polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons