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Title: vector calculus
Description: It includes vector algebra, gradient, level surface, del operator, divergence, curl, laplacian notation, integral calculus, surface integrals, volume integrals, fundamental theorem of calculus, fundamental theorem of gradient, divergence theorem, stokes' theorem, vectors expressed in curvilinear coordinates, divergence, gradient and curl in curvilinear coordinate system, helmholtz theorem.
Description: It includes vector algebra, gradient, level surface, del operator, divergence, curl, laplacian notation, integral calculus, surface integrals, volume integrals, fundamental theorem of calculus, fundamental theorem of gradient, divergence theorem, stokes' theorem, vectors expressed in curvilinear coordinates, divergence, gradient and curl in curvilinear coordinate system, helmholtz theorem.
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Gradient tells us how the field changes around a given
point
...
Level surfaces are also
called isosurfaces
...
g
...
It’s important to identify and analyze what happens with
the field around them because differentiation or
integration around them may fail!
For example gradient may not be defined there
...
What is the geometrical meaning of the divergence?
Patience!
Curl is the second of the two combinations of partial
derivatives which characterize the space variation of vector
What is the geometrical meaning of the curl? Patience!
Suppose I applied the del to some field, vector or scalar
...
Now if I apply the del to the new
field what will I get?
Laplace
The fundamental theorem of calculus
P
From
Feynman’s lectures
From Purcell's Electricity and Magnetism
To convert vectors initially expressed in Cartesian coordinates to
cylindrical coordinates…
Title: vector calculus
Description: It includes vector algebra, gradient, level surface, del operator, divergence, curl, laplacian notation, integral calculus, surface integrals, volume integrals, fundamental theorem of calculus, fundamental theorem of gradient, divergence theorem, stokes' theorem, vectors expressed in curvilinear coordinates, divergence, gradient and curl in curvilinear coordinate system, helmholtz theorem.
Description: It includes vector algebra, gradient, level surface, del operator, divergence, curl, laplacian notation, integral calculus, surface integrals, volume integrals, fundamental theorem of calculus, fundamental theorem of gradient, divergence theorem, stokes' theorem, vectors expressed in curvilinear coordinates, divergence, gradient and curl in curvilinear coordinate system, helmholtz theorem.