Integration on manifolds | Differential geometry | Determinants | Differential forms | Riemannian manifolds | Riemannian geometry
In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold of dimension , a volume form is an -form. It is an element of the space of sections of the line bundle , denoted as . A manifold admits a nowhere-vanishing volume form if and only if it is orientable. An orientable manifold has infinitely many volume forms, since multiplying a volume form by a function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density. A volume form provides a means to define the integral of a function on a differentiable manifold. In other words, a volume form gives rise to a measure with respect to which functions can be integrated by the appropriate Lebesgue integral. The absolute value of a volume form is a volume element, which is also known variously as a twisted volume form or pseudo-volume form. It also defines a measure, but exists on any differentiable manifold, orientable or not. Kähler manifolds, being complex manifolds, are naturally oriented, and so possess a volume form. More generally, the th exterior power of the symplectic form on a symplectic manifold is a volume form. Many classes of manifolds have canonical volume forms: they have extra structure which allows the choice of a preferred volume form. Oriented pseudo-Riemannian manifolds have an associated canonical volume form. (Wikipedia).
This video introduces volume and shows how to determine the volume of a cube and rectangular solid. http://mathispower4u.com
From playlist Volume and Surface Area (Geometry)
This video provides a basic introduction to volume.
From playlist Volume and Surface Area (Geometry)
Volume and Capacity (Converting between units of volume)
More resources available at www.misterwootube.com
From playlist Applications of Measurement
Cylinder Volume WITHOUT A Radius or Height!! (Chemistry)
Can we calculate the volume of this cylinder without any dimensions?? #physics #chemistry #NicholasGKK #tiktok #shorts
From playlist Heat and Chemistry
Determine the Volume of a Cube (Decimals)
This video explains how to determine the volume of a rectangular cube. http://mathispower4u.com
From playlist Volume and Surface Area (Geometry)
More resources available at www.misterwootube.com
From playlist Applications of Measurement
"Find the volume of more complex compound 3D shapes."
From playlist Shape: Volume & Surface Area
Geometry – Volume & Surface Area
Worked out examples involving volume and surface area.
From playlist Geometry
Another practice problem dealing with the volume of a sphere
From playlist Middle School - Worked Examples
What is a Tensor? Lesson 36: Other Notions of Duality
What is a Tensor? Lesson 36: Other Notions of Duality
From playlist What is a Tensor?
8ECM Invited Lecture: Robert Berman
From playlist 8ECM Invited Lectures
calculus introduction to volume
This video demonstrates how to visualize three-dimensional solids and how to set up their volume integrals.
From playlist Summer of Math Exposition Youtube Videos
Lecture 4: k-Forms (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
Lec 21 | MIT 3.091 Introduction to Solid State Chemistry
Engineered Glasses: Network Formers, Network Modifiers, Intermediates Properties of Silicate Glasses Metallic Glass View the complete course at: http://ocw.mit.edu/3-091F04 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.e
From playlist MIT 3.091 Introduction to Solid State Chemistry, Fall 2004
Lectures from Olin College Transport Phenomena course. Introduction to control volumes for conservation of mass and momentum.
From playlist Lectures for Transport Phenomena course
Theoretical aspects of hydraulic jump
Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 3
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 3 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Understanding the Volume of a Sphere Formula [Using High School Geometry]
Deriving the volume of a sphere formula. (4/3)πr(cubed) gives you the volume of a sphere, but where does the formula come from? Here is a simple explanation using geometry and algebra. The volume of a sphere is the measurement of the space it can occupy. A sphere is a three-dimensional sha
From playlist Math formulas, proofs, ideas explained
Andreas Bernig: Intrinsic volumes on pseudo-Riemannian manifolds
The intrinsic volumes in Euclidean space can be defined via Steiner’s tube formula and were characterized by Hadwiger as the unique continuous, translation and rotation invariant valuations. By the Weyl principle, their extension to Riemannian manifolds behaves naturally under isometric em
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects