What is the application of gradient and divergence of vector analysis
in computer science and engineering
Answers
Answer:
Brainiest me
Explanation:
Vector calculus owes much of its importance in engineering and physics to the gradient, divergence, and curl. These terms are used for simplifying the complicated vectors. Gradient, divergence, and curl are basic in connection with fields.
We all know that a scalar field can be solved more easily as compared to the vector field. Therefore, it is better to convert a vector field to a scalar field. Not all vector fields can be changed to a scalar field; however, many of them can be changed.
The relation between the two types of fields is accomplished by the term gradient. Hence, the gradient of a vector field has great importance for solving them.
The gradient ‘grad f’ of a given scalar function f(x, y, z) is the vector function expressed as
Grad f = (df/dx) i + (df/dy) j + (df/dz) k
We can also show the above formula in terms of ‘nabla’ and the new form of this formula is expressed by the image below.
Let us discuss an example.
If a function is a f(x, y, z) = 2x+ yz – 3y2, then grad f= f= 2i+ (z-6y)j+ yk. Actually, the term df/dx is the partial differentiation with respect to variable x.