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).
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
Gradient (1 of 3: Developing the formula)
More resources available at www.misterwootube.com
From playlist Further Linear Relationships
Determining a Unit Normal Vector to a Surface
http://mathispower4u.wordpress.com/
From playlist Vectors
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
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
What is Gradient, and Gradient Given Two Points
"Find the gradient of a line given two points."
From playlist Algebra: Straight Line Graphs
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
This video explains what information the gradient provides about a given function. http://mathispower4u.wordpress.com/
From playlist Functions of Several Variables - Calculus
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
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
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
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]
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
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]
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