Vector calculus | Surfaces

Surface gradient

In vector calculus, the surface gradient is a vector differential operator that is similar to the conventional gradient. The distinction is that the surface gradient takes effect along a surface. For a surface in a scalar field , the surface gradient is defined and notated as where is a unit normal to the surface. Examining the definition shows that the surface gradient is the (conventional) gradient with the component normal to the surface removed (subtracted), hence this gradient is tangent to the surface. In other words, the surface gradient is the orthographic projection of the gradient onto the surface. The surface gradient arises whenever the gradient of a quantity over a surface is important. In the study of capillary surfaces for example, the gradient of spatially varying surface tension doesn't make much sense, however the surface gradient does and serves certain purposes. (Wikipedia).

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MATH2018 Lecture 2.4 Level Surfaces, Tangent Planes, and Normal Lines

We discuss how the gradient of a scalar field is related to the concept of a level surface, and show how we can use it to define the tangent plane and normal line at a point.

From playlist MATH2018 Engineering Mathematics 2D

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Gradient (1 of 3: Developing the formula)

More resources available at www.misterwootube.com

From playlist Further Linear Relationships

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Determining a Unit Normal Vector to a Surface

http://mathispower4u.wordpress.com/

From playlist Vectors

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Show the Gradient to a Surface Using 3D Calc Plotter

New url for the 3D plotter: https://c3d.libretexts.org/CalcPlot3D/index.html This video using 3D Calc Plotter to illustrate the meaning of a gradient vector. http://mathispower4u.com

From playlist 3D Calc Plotter

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11_7_1 Potential Function of a Vector Field Part 1

The gradient of a function is a vector. n-Dimensional space can be filled up with countless vectors as values as inserted into a gradient function. This is then referred to as a vector field. Some vector fields have potential functions. In this video we start to look at how to calculat

From playlist Advanced Calculus / Multivariable Calculus

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12mat Graphs Straight Line

Gradient - y Intercept

From playlist 2014 12mat

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What is Gradient, and Gradient Given Two Points

"Find the gradient of a line given two points."

From playlist Algebra: Straight Line Graphs

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MATH2018 Lecture 2.3 Gradient and Directional Derivative

We introduce the concepts of the gradient and directional derivative, which tell us how a scalar field varies in space.

From playlist MATH2018 Engineering Mathematics 2D

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The Gradient

This video explains what information the gradient provides about a given function. http://mathispower4u.wordpress.com/

From playlist Functions of Several Variables - Calculus

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Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07

Lecture 12: Gradient; directional derivative; tangent plane. View the complete course at: http://ocw.mit.edu/18-02SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.02 Multivariable Calculus, Fall 2007

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Worldwide Calculus: Level Sets & Gradient Values

Lecture on 'Level Sets & Gradient Values' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.

From playlist Multivariable Derivatives

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Lecture 17: Discrete Curvature II (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

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Lecture 8A : A brief overview of "Hessian Free" optimization

Neural Networks for Machine Learning by Geoffrey Hinton [Coursera 2013] Lecture 8A : A brief overview of "Hessian Free" optimization

From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]

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Lecture 8.1 — A brief overview of Hessian-free optimization [Neural Networks for Machine Learning]

Lecture from the course Neural Networks for Machine Learning, as taught by Geoffrey Hinton (University of Toronto) on Coursera in 2012. Link to the course (login required): https://class.coursera.org/neuralnets-2012-001

From playlist [Coursera] Neural Networks for Machine Learning — Geoffrey Hinton

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Lecture 6/16 : Optimization: How to make the learning go faster

Neural Networks for Machine Learning by Geoffrey Hinton [Coursera 2013] 6A Overview of mini-batch gradient descent 6B A bag of tricks for mini-batch gradient descent 6C The momentum method 6D A separate, adaptive learning rate for each connection 6E rmsprop: Divide the gradient by a runni

From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]

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Repulsive Shape Optimization

In visual computing, point locations are often optimized using a "repulsive" energy, to obtain a nice uniform distribution for tasks ranging from image stippling to mesh generation to fluid simulation. But how do you perform this same kind of repulsive optimization on curves and surfaces?

From playlist Repulsive Videos

Related pages

Differential operator | Scalar field | Grade (slope) | Surface (mathematics) | Gradient | Vector calculus | Orthographic projection | Spatial gradient