In this section, we will learn about the Gradient, Directional Derivative, Divergence, and Curl of a function. Each topic is covered with the help of video lectures and each topic has an example question to make the concept crisp and clear.
Gradient of a Scalar Point Function
The gradient of a scalar point function at a particular point is normal at that point. We calculate gradient vector by multiplying del vector and scalar function. There can be two normals to the curve at a point, one is outward and another is inward. Normals can be calculated with the help of the gradient formula. Watch the given video tutorials to learn the gradient of the function.
Directional Derivative of a Scalar Point Function
Directional derivative is the projection of the gradient vector along the given vector. Hence, the maximal directional derivative of the scalar field is in the direction of the gradient vector itself. Also, the gradient vector gives the maximum rate of change of function. Watch the given video lecture to learn the concept of directional derivative.
Divergence of a Vector Point Function
We calculate divergence of a function by takin dot product of
Curl of a Vector Point Function
We find the curl of a vector point function by cross multiplying the del vector and vector function. Learn this concept with the help of an illustrative example with the help of the video lecture given below.
That’s all for this section. Watch the video lectures on repeat mode to grasp the topic thoroughly. Comment on the page or contact us for any queries or doubts and we will answer them ASAP. You can also suggest the topics to be covered on our next videos by contacting us.