List engineering applications of “Scalar Fields” and “Vector Fields”. Explain in which courses you have learned...

List engineering applications of “Scalar Fields” and “Vector Fields”.

Explain in which courses you have learned about the applications of these fields.

(What is a Tensor? and have you heard about Tensor fields?).

Explain the meaning of the term “Conservative” and its applications. What is the relation between this term and the operators Gradient and Curl?

Solutions

Expert Solution

Some industrial applications of scalar fields and vector fields are:-

1)Geometric processing of surfaces

2)Computational fluid dynamics

3)Electro dynamic simulations

4)Non photo realistic rendering

5)Texture synthesis

6)Scalar fields are used to describe gravitation fields( commonly used in higgs mechanism)

#you can write your own course where you have the given chapters to study (I have learned about Scalar and vector fields in calculus during graduation and applications in physics semester 3.)

Tensor: A tenor is a mathematical representation of a scalar and a multi dimensional matrix or array. A tensor may consist of a single number, in which case the tensor is said to be of the order zero (which is simply a scalar), a 2-D matrix would be a vector and so on and so forth.

Tensor field is basically a generalization of Scalar and vector fields, i.e. it will assign a scalar and vector to each point of space.

Conservative means the integral path of is independent. This path independence with the line integral is equivalent to the vector or any dimensional field being conservative.

genius_generous answered 1 month ago

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