Difference between revisions of "The Road to Reality Study Notes"

The amazing result here is that a general contour from $$a$$ to $$b$$ for the function <math>\frac{1}{z}</math> has be rephrased and shown to be equal to the result for a ''closed contour'' that loops around the point of non-analyticity (the origin in this case), regardless of where the points $$a$$ and $$b$$ (or the point of non-analyticity) lie in the complex plane.  Note that since $$logz$$ is multi-valued, we need to specify the actual closed contour being used (if we looped twice rather than once, then the answer is different).

The amazing result here is that a general contour from $$a$$ to $$b$$ for the function <math>\frac{1}{z}</math> has be rephrased and shown to be equal to the result for a ''closed contour'' that loops around the point of non-analyticity (the origin in this case), regardless of where the points $$a$$ and $$b$$ (or the point of non-analyticity) lie in the complex plane.  Note that since $$logz$$ is multi-valued, we need to specify the actual closed contour being used (if we looped twice rather than once, then the answer is different).

== Chapter 8 Riemann surfaces and complex mappings ==

== Chapter 8 Riemann surfaces and complex mappings ==