Uploaded April 2020 | Updated September 2026, 2 weeks ago
This video covers #ComplexIntegration of a natural logarithm using #BranchCuts to convert the natural log from a multiple-valued function to a single-valued function. This integration involved using an elaborately constructed contour, the #ResidueTheorem, and the ML inequality (link: youtube.com/watch?v=sEyVa_W1Syo&list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB&index=5&t=0s) to arrive at the final answer.
Questions/requests? Let me know in the comments!
Pre-reqs: Every video before this one in my #ComplexVariables playlist, especially the video on Branch Points and Branch Cuts right before this: youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB
Lecture Notes: drive.google.com/open?id=1JHiTM9r6liwQDz9XTE_lUmhe3najPJ1h
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
Cesar Garza
Daigo Saito
Alvin Barnabas
Damjan
Yenyo Pal
Lisa Bouchard
Patapom
Gabriel Sommer
Eugene Bulkin
Adam Pesl
Yiu Chong
René Gastelumendi
EDIT: Note that at 9:00, there should be a less than or equal to sign, since the modulus of the integral is less than or equal to the integral of the modulus. Thanks to some of the commenters below for pointing that out!
This video covers #ComplexIntegration of a natural logarithm using #BranchCuts to convert the natural log from a multiple-valued function to a single-valued function. This integration involved using an elaborately constructed contour, the #ResidueTheorem, and the ML inequality (link: youtube.com/watch?v=sEyVa_W1Syo&list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB&index=5&t=0s) to arrive at the final answer.
Questions/requests? Let me know in the comments!
Pre-reqs: Every video before this one in my #ComplexVariables playlist, especially the video on Branch Points and Branch Cuts right before this: youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB
Lecture Notes: drive.google.com/open?id=1JHiTM9r6liwQDz9XTE_lUmhe3najPJ1h
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
Cesar Garza
Daigo Saito
Alvin Barnabas
Damjan
Yenyo Pal
Lisa Bouchard
Patapom
Gabriel Sommer
Eugene Bulkin
Adam Pesl
Yiu Chong
René Gastelumendi
EDIT: Note that at 9:00, there should be a less than or equal to sign, since the modulus of the integral is less than or equal to the integral of the modulus. Thanks to some of the commenters below for pointing that out!
