Thanks for responding.
I can start with a closed line integral and by multiplying by 1 either dx/dx or dy/dy and the fundamental theorem cal end up with Green's Theorem. I can also see the k component of the curl in this so I have no problem going to stokes theorem.
I'm am though having...
If you start with the two dimensional green's theorem, and you want to extend this three dimensions.
F=<P,Q>
Closed line integral = Surface Integral of the partials (dP/dx + dQ/dy) da
seems to leads the divergence theorem,
When the space is extended to three dimensions.
On the...
If you start with the two dimensional green's theorem, and you want to extend this three dimensions.
F=<P,Q>
Closed line integral = Surface Integral of the partials (dP/dx + dQ/dy) da
seems to leads the divergence theorem,
When the space is extended to three dimensions.
On the...
made the graph a little better
After calculating the normal and bi normal vector I adjusted the final parameters:
I used 0.1v with v from 0 to 500
This made the curve look a little crisper, but it still has its problems.
The final fernet equation using the normal and bi-normal vectors...
I have recently been working in Mathematica 6.0 trying to graph various curves using ParametricPlot3D. I have specifically defined:
a1[p_]={(sqrt(25-p^2))*Sin[10*p],(Sqrt(25-p^2))*Cos[10*p],(p)^2};
Graphing this is no problem.
The problem is I am trying to turn this into a Fernet type...
Pursuit Problem:
A Frisbee is 40 ft north and 30 ft east of a dog.
The Frisbee is traveling north at 5 ft sec.
The dog can run at constant 10 ft/sec = SQRT( (Vdx)^2 + (Vdy)^2 )
Tan(angle)=Y(t)/X(t)
As the dog runs towards the Frisbee, the dog from “instinct” keeps the angle...
Maybe a little longer approach,
But this is the way I’d approach this in a cal 2 class
Please excuse the notation.
First rewrite integral sqrt(X)/sqrt(1+CX) dx
Now let 1/x =u^2
dx=-2/(1/u^3)du
also let a^2 = c to make notation a little easier to work with.
This will yield an...
I am a physicist, not a mathematician.
This problem has bothered me for 40 years.
All introductory Calculus texts would consider this integral divergent.
An example found in many texts is the integral of 1/(x-2) from 0 to 3, which is just a variant to the question I am asking. What I find...