Complex Integration Using Branch Cuts

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: Complex Integration: The ML Inequalit...) 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: Complex Variables and Functions

Lecture Notes: https://drive.google.com/open?id=1JHi...
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Twitter: Twitter: 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!

• #education
• #complex_variables
• #complex_analysis
• #math
• #applied_math
• #mathematics
• #complex_calculus
• #complex_functions
• #complex_log
• #branch_point
• #branch_cut
• #branch_points
• #branch_cuts
• #complex_integration
• #complex_natural_logarithm
• #complex_natural_log
• #integration_branch_cuts
• #integration_branch_points
• #log_integration