Understanding the Gradient Theorem for Vector Calculus Problems

[math_04]

Homework Statement

Check the gradient theorem for the scalar field T= x^2 + 4xy + 2yz^3 and the paths

a) (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)

Homework Equations

Equations = none well maybe divergence of a vector field= (df/dx)*x + (df/dy)*y + (df/dz)* z where x,y and z are vectors.

The Attempt at a Solution

This is actually from a tutorial in electromagnetism, and from reading Griffiths introduction to electrodynamics, the following definition is given for gradient theorem.

T(b) - T(a) = integral of the dot product of del T and dl.

Ok, I gave a shot at the solution and tried to solve it, got it wrong, tried to write up the solution here and gave up because it would be hard to understand without symbols.

All I need to know is whether there are better resources on the web to help solve these kind of problems (well explained examples etc). Unfortunately, Griffiths's examples arent great and very poorly explained which leaves me totally baffled

 

[slider142]

It sounds like you need more experience in doing vector calculus problems. Try "div grad curl and all that" by Schey. If you need online examples, a quick search of Google for "vector calculus" gives many good results.