We know that mathematicians study different mathematical spaces such as Hilbert space, Banach space, Sobolev space, etc...
but as engineers, is it necessary for us to understand the definition of these spaces?
I dont think so. Even many physicists do not know all these definitions, except perhaps Hilbert space.
Detailed knowledge on foundation is necessary for a civil engineer to construct a building structure on the founation. Engineering means application of science for industrial purpose .
For a name sake engineer who works as technician or supervisor, the knowledge on definition is not mandatory.
The definition of Banach space is easier than one of Hilbert.
Sobolev space is much more delicate. This space is needed to say an existence of a solution of some differential equation.
You and many physician believe the existence, so it is not needed.
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