Shorthand Notation in Vector Equations

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Shorthand Notation in Vector Equations
partial differential operator Means
differentiate contents of brackets with respect
to x and treating all other variables as constants
Scalar product By definition the scalar product
of two vectors A (A (Ax,Ay,Az)) and B ( B
(Bx,By,Bz)) is given by
where q is the angle between the two vectors A
and B.
Vector product By definition the vector product
of two vectors A and B is given by
where i, j, k are unit vectors in the x, y, z
dir., respectively
Unit vector perpendicular to A and B
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We can define a vector operator called del ,
written as
It is more complicated than normal
partial differentials as it is a vector !
We can define the product of del with a scalar f
as
The scalar product of del with a vector V is
known as the divergence of V, and is written as
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We define the curl of V as
Flat brackets mean take determinant
Another important expression is del squared,
also known as the Laplacian
Useful books are Maths - Mathematical methods
in the physical sciences by Mary L. Boas
Mathematical methods for science
students by G. Stephenson Engineering- Introdu
ction to transport phenomena by W.J. Thomson