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Contour Integration #6 - Integrating log(x)/(x^2 + 1) - LearnMathsFree


Contour Integration #6 - Integrating log(x)/(x^2 + 1) - LearnMathsFree

NOTE: I made an error when taking the limit of arctan(x) as x approaches infinity. It should be pi/2, not pi/4. The imaginary parts of both sides would then cancel. (But it doesn't matter, because the integral we were evaluating was purely real.) In this video, we look at a more involved example of a contour integral. We explain how to take branch cuts using principal and non-principal definitions of the complex logarithm Log(z). We evaluate the integral using the method of contour integration, by using an indented semi-circular contour. We then use the residue theorem, together with the estimation lemma, to derive the required result. More to follow. Video on the complex logarithm: https://www.youtube.com/watch?v=cvo6ROtY_8c Like us on Facebook: https://www.facebook.com/learnmathsfree Follow us on Twitter: https://twitter.com/LearnMathsFree Google+: https://plus.google.com/u/0/b/117033642523061853672/117033642523061853672 Video URL: https://youtu.be/zyzlvT7BLCo Channel URL: https://www.youtube.com/channel/UCtTFrEPIqaKfWyGkBi9Rmvg
動画ID:zyzlvT7BLCo
投稿日時:2016年08月8日 00時22分
再生回数:8,750 回
コメント数:16
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低く評価した人の数:6人


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