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On problem 2. I am breaking the curve <math>\gamma</math> up into two piece wise curves <math>\gamma_1</math> and <math>\gamma_2</math> that meet when the curve <math>\gamma</math> crosses the negative real axis at the point <math>z_0</math>. I then am taking the principle branch of log as an analytic function to evaluate the two curves with the Log <math>{z_0}</math> values dropping out. My worry is that since <math>z_0</math> sits on the branch cut that the function won't be analytic for one of the endpoints of the curves. Am I getting myself into trouble with this?--[[User:Rgilhamw|Rgilhamw]] 21:13, 8 December 2009 (UTC--[[User:Rgilhamw|Rgilhamw]] 18:29, 9 December 2009 (UTC)) | On problem 2. I am breaking the curve <math>\gamma</math> up into two piece wise curves <math>\gamma_1</math> and <math>\gamma_2</math> that meet when the curve <math>\gamma</math> crosses the negative real axis at the point <math>z_0</math>. I then am taking the principle branch of log as an analytic function to evaluate the two curves with the Log <math>{z_0}</math> values dropping out. My worry is that since <math>z_0</math> sits on the branch cut that the function won't be analytic for one of the endpoints of the curves. Am I getting myself into trouble with this?--[[User:Rgilhamw|Rgilhamw]] 21:13, 8 December 2009 (UTC--[[User:Rgilhamw|Rgilhamw]] 18:29, 9 December 2009 (UTC)) | ||
| − | for anyone who had the same question, Prof. Bell covered this in class today. Having the point where the curves break on the branch cut will not work, so it needs to be chopped up into more piece-wise curves. | + | for anyone who had the same question, Prof. Bell covered this in class today. Having the point where the curves break on the branch cut will not work, so it needs to be chopped up into more piece-wise curves.--[[User:Rgilhamw|Rgilhamw]] 18:29, 9 December 2009 (UTC) |
Revision as of 13:29, 9 December 2009
Discussion area to prepare for the Final Exam
On problem 2. I am breaking the curve $ \gamma $ up into two piece wise curves $ \gamma_1 $ and $ \gamma_2 $ that meet when the curve $ \gamma $ crosses the negative real axis at the point $ z_0 $. I then am taking the principle branch of log as an analytic function to evaluate the two curves with the Log $ {z_0} $ values dropping out. My worry is that since $ z_0 $ sits on the branch cut that the function won't be analytic for one of the endpoints of the curves. Am I getting myself into trouble with this?--Rgilhamw 21:13, 8 December 2009 (UTC--Rgilhamw 18:29, 9 December 2009 (UTC))
for anyone who had the same question, Prof. Bell covered this in class today. Having the point where the curves break on the branch cut will not work, so it needs to be chopped up into more piece-wise curves.--Rgilhamw 18:29, 9 December 2009 (UTC)
