Scalars | Differential geometry | Rates | Differential calculus | Generalizations of the derivative | Multivariable calculus
In mathematics, the directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. The directional derivative of a scalar function f with respect to a vector v at a point (e.g., position) x may be denoted by any of the following: It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordinates being constant.The directional derivative is a special case of the Gateaux derivative. (Wikipedia).
11_5_1 Directional Derivative of a Multivariable Function Part 1
Understanding that a partial derivative refers to a rate of change in the direction of a certain axis, we now look at the rate of change in any direction. The direction is indicated by a unit vector, in other words it has a dimension of one and is therefore only its direction is important
From playlist Advanced Calculus / Multivariable Calculus
Directional derivative of f(x,y)
Free ebook http://tinyurl.com/EngMathYT I present an example where I calculate the derivative of a function of two variables in a particular direction. In particular, I take the derivative of $f(x,y) := 1 - x^2/2 - y^4/4$ in the direction of the vector ${\bf u} := (1,1)$. I solve the
From playlist Engineering Mathematics
Directional Derivatives | What's the slope in any direction?
A directional derivative gives the slope in any particular direction, similar to partial derivatives which give the slope just in the x or y directions. We formally define directional derivatives by modifying the familiar limit definition of the derivative for when you move along some vect
Multivariable Calculus | The gradient and directional derivatives.
We define the gradient of a function and show how it is helpful in finding the directional derivative. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
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From playlist Functions of Several Variables - Calculus
Gradient and directional derivative
Free ebook http://tinyurl.com/EngMathYT A lecture on the gradient and directional derivative of functions of two (or more) variables. Plenty of examples are discussed. The ideas find uses in applied mathematics, science and engineering.
From playlist Mathematics for Finance & Actuarial Studies 2
Multivariable Calculus | The directional derivative.
We give the formal definition of the directional derivative as well as some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Directional derivative example
Example on directional derivative of a function of two variables.
From playlist Engineering Mathematics
14: Directional Derivatives and Gradient - Valuable Vector Calculus
Explanation of directional derivatives as a dot product and how they relate to the gradient vector. We also talk about contour lines! Full Valuable Vector Calculus playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1 New math videos every Monday and Friday.
From playlist Valuable Vector Calculus
Worldwide Calculus: The Directional Derivative
Lecture on 'The Directional Derivative' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
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
How To Find The Directional Derivative and The Gradient Vector
This Calculus 3 video tutorial explains how to find the directional derivative and the gradient vector. The directional derivative is the product of the gradient vector and the unit vector. To find the gradient vector, you need to find the partial derivatives of f with respect to x, y, a
From playlist New Calculus Video Playlist
MATH2018 Lecture 2.1 Extreme Values
We extend the second derivative test to find maxima and minima of functions of more than one variable.
From playlist MATH2018 Engineering Mathematics 2D
Calculus 14.6 Directional Derivatives and the Gradient
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Introduction to Directional Derivatives - Calculus 3
Introduction to Directional Derivatives - Calculus 3
From playlist Calculus 3
Partial Derivatives and Chain Rule
We discuss partial derivatives, the 1-dimensional Chain Rule, and the Chain Rule involving partial derivatives.
From playlist Mathematical Physics II Uploads