Analytic Continuation I The Identity Theorem I Complex Analysis #26

Analytic Continuation and the Identity theorem in Complex Analysis explained. Analytic continuation is a method to expand the domain of an analytic function and the Identity theorem tells us everything we need to know about analytic functions. The Identity Theorem is lowkey the greatest theorem in the whole course (fight me). It simply lets us know a function's behavior in the whole domain by knowing it on some part in the domain - that is powerful. It is so great that I had to learn how to animate a motion graphic award to make it justice, which took a while... The video will include concepts as: ► The Identity Theorem ► Analytic Continuation ► Accumulation Point LINK TO COMPLEX ANALYSIS PLAYLIST https://youtube.com/playlist?list=PLraTC6fSWOiptqOd_rMhFk6mZM30l7SqQ LINK TO CANVAS https://drive.google.com/file/d/1-0nkCRIRSxPLs2ZjLSUnFWKfkurSLAzG/view?usp=sharing SUPPORT Consider subscribing, liking, or leaving a comment, if you enjoyed the video or if it helped you understand the subject. It really helps me a lot. TIMESTAMPS 00:00 - 00:36 Definition Analytic Continuation 00:36 - 01:20 The implications of Analytic Continuation 01:20 - 02:20 Good things to know 02:20 - 03:38 The Identity Theorem 03:38 - 06:04 Accumulation Point and Subset of Zeros 06:04 - 06:13 Only the greatest statement in the whole course 06:13 - 07:35 The Identity Theorem for Analytic Functions 07:35 - 08:59 The Identity Theorem's use for Analytic Continuation 08:59 - 09:50 Analytic Continuation along a path 09:50 -12:22 Example Analytic Continuation along a path 12:22 - 12:43 Outro SOCIAL ► Follow me on Youtube: http://bit.ly/1NQhPJ9 ► Follow me on Twitter: https://twitter.com/The_MathCoach HASHTAGS #TheMathCoach #ComplexAnalysis #Complex Analysis Playlist