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The Road to Reality Study Notes: Difference between revisions
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An example of this rigidity and path dependence is ‘our old friend’ \(logz\). There is no power series expansion about the origin due to the singularity there but depending on the path chosen of points around the origin (clockwise or anti-clockwise) the function extends or subtracts in value by \(2πi\). See chapter 5 and the euler formula (\(e^{πi}=-1\)) for a refresher. | An example of this rigidity and path dependence is ‘our old friend’ \(logz\). There is no power series expansion about the origin due to the singularity there but depending on the path chosen of points around the origin (clockwise or anti-clockwise) the function extends or subtracts in value by \(2πi\). See chapter 5 and the euler formula (\(e^{πi}=-1\)) for a refresher. | ||
== Chapter | == Chapter 8 Riemann surfaces and complex mappings == | ||
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