To determine.To fill: a) The blank in the statement "Del operator: displaystylenabla=?" b) The blank in the statement "Gradient: displaystylenabla{f}=?" c) The blank in the "Laplacian: displaystylenabla^{2}{f}=?"

Tabansi 2020-12-16 Answered
To determine.To fill:
a) The blank in the statement "Del operator: =?"
b) The blank in the statement "Gradient: f=?"
c) The blank in the "Laplacian: 2f=?"
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

jlo2niT
Answered 2020-12-17 Author has 96 answers

a)
In Cartesian coordinate syste, Rn with coordinates (x1,,xn) and standard basis
{e1,,en},
is defined in terms of partial derivative operators as:
=i=1neixi
=(x1,,xn
However, del can also be expressed in other coordinate systems.
Therefore, the complete statement is "Del operator: =i=1neixi".
b)
In Cartesian coordinate system Rn with coordinates ((x1,,xn) and respective partial derivatives:
f=xf(x)
=[f(x)x1,,f(x)xn]T
Therefore, the complete statement is "Gradient: f=[f(x)x1,,f(x)xn]T".
c)
Laplacian operator is defined as:
2f=2fx2+2fy2+2fz2
Therefore, the comlete statement is "Laplacian: 2f=2fx2+2fy2+2fz2.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more