I understand the concept behind continuous deformations.(adsbygoogle = window.adsbygoogle || []).push({});

Say we have two curves ζ1 and ζ2 from A to B on some domain D and say that Pdx + Qdy is closed. Say we can show n points A=c1,c2,...,cn=B and A=d1,d2,d3,...,dn=B, so that we can first say follow the curve ζ1 from A to c1 then over to d1 by means of straight line l1 (call this modified curve θ1), and then up to B, and then we can also look at following ζ1 from A to c2 then over to d2 by means of line l2 and then up to B (call this θ2), say that if l1 and l2 are contained in a rectangle in the domain D, then we know that because the rectangle is star shaped and Pdx +Qdy is closed on D that ∫Pdx+dy on θ1 and ∫Px+dy on θ2 are both path independent on that rectangle. So those two integrals are the same. We can do this n times and eventually end up with the fact that ∫Pdx + Qdy on ζ1 = ∫Pdx+Qdy on ζ2.

Now, I keep seeing questions that say things like "specify exactly the family of paths that can deform ζ1 continuously to ζ2". I am so lost at things like this. My prof gave me this formula: δ(t,s)=δ_{1}(t)(1-s) + δ_{2}(t)s for 0 ≤ s ≤ 1

I am so confused by what exactly this equatino is and just understanding these family of curves. From my understanding of what continuous deformation is it seems like you are picking n points. So wouldn't you be having n curves? I'm so confused

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Continuous deformation? Family of curves? So confused!

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**