Vector fields and integral curves


by meteorologist1
Tags: curves, fields, integral, vector
meteorologist1
meteorologist1 is offline
#1
Jan10-05, 07:06 PM
P: 101
I'm studying about vector fields and integral curves in the space R^n.

I need some help in proving or getting some comments/feedback on the following propositions:

1) Find a proof or counterexample: Let K and K' be two vector fields on R^n such that every integral curve of K is also an integral curve of K'. Then K = K'.

2) State and prove a theorem to the effect that integral curves of a vector field can never cross.

3) Let K be a vector field, and [tex] \alpha [/tex] a positive function on R^n. Express the integral curves of the vector field [tex] \alpha K [/tex] in terms of those of K. And why did we require that [tex] \alpha [/tex] be positive?

Thanks in advance.
Phys.Org News Partner Mathematics news on Phys.org
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race

Register to reply

Related Discussions
Vector Fields and Vector Bundles Differential Geometry 7
Line integral and vector fields Calculus & Beyond Homework 2
Space Curves --> Unit Tangent Vector and Curvature Calculus 2
Vector Fields Calculus 3
2 curves in an integral Introductory Physics Homework 1