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
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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
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