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Lecture

# The Gradient Vector - Notation and Definition

Home > Mathematics > Calculus > Multivariable Calculus > The Gradient Vector - Notation and Definition Lecture Details:

The Gradient Vector - Notation and Definition. In this video, I talk about the directional derivative, and the corresponding definition of the gradient vector. Nothing deep here!! Just a small observation and some notation!

Lectures:
• ### The Cross Product

00:08:05

In this video, I give the formula for the cross product of two vectors, discuss geometrically what the cross product is, and do an example of finding the cross product.

• ### Finding the Scalar Equation of a Plane

00:07:40Patrick Jones

Finding the Scalar Equation of a Plane - In this video, I discuss the formula to find the scalar equation of a plane, how to derive it, and a simple example using it!

• ### Torque - An Application of the Cross Product

00:04:12Patrick Jones

Torque - When you tighten a bolt on the tire of your car, you are using torque! An application of the cross product involving torque is shown. In this video, I calculate the magnitude of the torque vector.

• ### Finding the Point Where a Line Intersects a Plane

00:05:38Patrick Jones

Finding the Point Where a Line Intersects a Plane - Multivariable Calculus Stuff!In this video, I find the point at which a line would intersect a plane.

• ### Finding the Domain of a Vector Function

00:06:20Patrick Jones

Finding the Domain of a Vector Function - In this video I find the domain of one vector function. Nothing too heavy here!

• ### Finding the Limit of a Vector Function

00:05:39Patrick Jones

Finding the Limit of a Vector Function - In this video I do one example of finding the limit of a vector function.

• ### The Arc Length of a Vector Function

00:07:43Patrick Jones

The Arc Length of a Vector Function - In this video I give the formula to find the arc length of a 3-dimensional vector function and do one concrete example of finding the length of a vector function.

• ### Multivariable Calculus: Showing a Limit Does NOT Exist

00:08:39Patrick Jones

Multivariable Calculus: Showing a Limit Does NOT Exist - In this video, I spend a bit of time talking about what it means for a limit not to exist and do one example showing that the limit does not exist.

• ### Multivariable Calculus: Finding and Sketching the Domain

00:06:21Patrick Jones

Multivariable Calculus: Finding and Sketching the Domain of a function z = f(x,y).I discuss the basic idea and do examples.

• ### Finding Partial Derviatives

00:07:12Patrick Jones

Finding Partial Derviatives - 3 examples are shown of finding partial derivatives of a multivariable function.

• ### Calculus: Higher Order Partial Derivatives

00:08:10Patrick Jones

Calculus: Higher Order Partial Derivatives. In this video, I briefly discuss the notation for higher order partial derivatives and do an example of finding a 3rd partial derivative.

• ### Tangent Plane Approximations

00:12:15Patrick Jones

In this video, I give the formula and use it to find a tangent plane approximation. Both the tangent plane and the actual numerical estimate are shown.

• ### General Chain Rule - Part 1

00:09:40Patrick Jones

General Chain Rule - Part 1 - In this video, I discuss the general version of the chain rule for a multivariable function. There will be a follow up video doing a few other examples as well!

• ### General Chain Rule - Part 2

00:06:41Patrick Jones

General Chain Rule - Part 2. In this video I finish off two examples of the general chain rule from Part 1.

• ### MultiVariable Calculus - Implicit Function Theorem

00:04:55Patrick Jones

Multivariable Calculus - Implicit Function Theorem.In this video, I show how to find partial derivatives of an implicitly defined multivariable function using the Implicit Function Theorem.

• ### MultiVariable Calculus - Implicit Differentiation

00:05:51Patrick Jones

MultiVariable Calculus - Implicit Differentiation.In this video, I point out a few things to remember about implicit differentiation and then find one partial derivative.

• ### MultiVariable Calculus - Implicit Differentiation - Ex 2

00:04:43Patrick Jones

MultiVariable Calculus - Implicit Differentiation - Ex 2.In this video, I do a follow up example where we find dz/dy.

• ### Finding the Directional Derivative

00:06:42Patrick Jones

Finding the Directional Derivative - In this video, I give the formula and do an example of finding the directional derivative that corresponds to a given angle.

• ### The Gradient Vector - Notation and Definition

00:02:13Patrick Jones

The Gradient Vector - Notation and Definition. In this video, I talk about the directional derivative, and the corresponding definition of the gradient vector. Nothing deep here!! Just a small observation and some notation!

• ### Local Maximum and Minimum Values/ Function of Two Variables

00:10:43Patrick Jones

Local Maximum and Minimum Values/ Function of Two Variables.An outline of the procedure, along with a complete example are shown.

• ### Local Maximum and Minimum Values -Function of Two Variables

00:06:10Patrick Jones

Local Maximum and Minimum Values/ Function of Two Variables.Another example is shown!

• ### Vector Functions: Position, Velocity, Acceleration Word Problem, Ex 1

00:03:23Patrick Jones

Vector Functions: Position, Velocity, Acceleration Word Problem, Ex . In this video, we are given the velocity vector of a car as well as its initial displacement. We have to find the position of the car after 1 second.

• ### Smooth Vector Functions, Ex 1

00:02:26Patrick Jones

Smooth Vector Functions, Ex 1. In this video, I show how to determine if a given curve is smooth or not.

• ### Smooth Vector Functions, Ex 2

00:04:19Patrick Jones

Smooth Vector Functions, Ex 2. Another example where we have to decide if a given vector function is smooth or not.

• ### Unit Tangent Vector at a Given Point

00:04:50Patrick Jones

Finding a Unit Tangent Vector at a Given Point. In this video, I find a unit tangent vector to a space curve at a given value of t.

• ### Derivative of a Vector Function - Another Ex 1

00:02:35Patrick Jones

Derivative of a Vector Function - Another Ex 1. In this video, I show an example of finding the derivative of a vector function. It is pretty simple: just take the derivative of each part!

• ### Finding the Limit of a Vector Function - Another Ex 1

00:01:46Patrick Jones

Finding the Limit of a Vector Function - Another Ex 1. In this video, I find the limit of a vector valued function.

• ### Finding the Limit of a Vector Function - Another Ex 2

00:04:04Patrick Jones

Finding the Limit of a Vector Function - Another Ex 2. In this video, I find the limit of another vector valued function. In this example I have to use both the Squeeze Theorem and also L'Hospital's rule.

• ### Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D

00:05:03Patrick Jones

Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D. Here I describe two lines in 3space using parametric equations. We have to decide if they coincide, are parallel, are skew or if they intersect in exactly one point.

• ### Parametric Equations of Line Passing Through a Point

00:02:07Patrick Jones

Parametric Equations of Line Passing Through a Point. In this video, I show how to find the parametric equations of a line that passes through a given point with a given direction vector.

• ### Orthogonal Projections - Scalar and Vector Projections

00:03:21Patrick Jones

Orthogonal Projections - Scalar and Vector Projections. In this video, we look at the idea of a scalar and vector projection of one vector onto another.

• ### Triple Integrals, Changing the Order of Integration, Part 1 of 3

00:12:52Patrick Jones

Triple Integrals, Changing the Order of Integration, Part 1 of 3. In this video, I start discussing how a particular order of integration for a given region and integral ' makes sense '! Then I go about changing the order of integration. In this part, we integrate with respect to z first.

• ### Triple Integrals, Changing the Order of Integration, Part 2 of 3

00:09:30Patrick Jones

Triple Integrals, Changing the Order of Integration, Part 2 of 3. In this video, I show how to integrate the region by integrating with respect to x first.

• ### Triple Integrals, Changing the Order of Integration, Part 3 of 3

00:12:53Patrick Jones

Triple Integrals, Changing the Order of Integration, Part 2 of 3. In this video, I show how to integrate the region by integrating with respect to y first.