#isolatedsingularity #definition #example #complexanalysis #mscmaths #maths #highermathematics

This video includes the important example and definition of isolated singularity.

Important playlists:

TAYLOR'S THEOREM proof and Examples

https://youtube.com/playlist?list=PLlNouZALEsH2bV7AZrMQuu4w2YcxR_sil&si=bpB62_eItcgYkjyA

Laurent's Theorem proof and Examples

https://youtube.com/playlist?list=PLlNouZALEsH1BF_pvFvECC-EiTG0WxIvO&si=9KgTaqfo95Is7eT4

Full Complex Analysis/ M.Sc
https://youtube.com/playlist?list=PLlNouZALEsH23kRaWCfE9Kw4oUOG4Il04&si=uoAjXGibkFPHsK9n

Singularity

https://youtube.com/playlist?list=PLlNouZALEsH3ZA9wi7DqyuFVMLT2U4vtj&si=ApQ3McOPcdCs-O_p

B.Sc / Differential Equations

https://youtube.com/playlist?list=PLlNouZALEsH35MHzSePZJfZOdPKo6Pbox&si=g4BxJ9ypeI2VLrnX

This video by Saloni Sharma provides an educational explanation of isolated singularities within the context of Complex Analysis.

Key takeaways include:

Definition of Isolated Singularity: A point z = a is considered an isolated singularity of a function f(z) if the function is not analytic at z = a, but is analytic in the deleted neighborhood of that point (meaning every point in the neighborhood except a itself) (0:43 - 2:13).
Key Condition: Essentially, this means there exists a surrounding area for z = a that contains no other singularities (1:55 - 2:09).

Examples provided:

f(z) = 1/z: The function is not defined at z = 0, making z = 0 an isolated singularity (2:24 - 3:01).
f(z) = 1/((z-1)(z-2)(z-3)): The points z = 1, 2, and 3 are all identified as isolated singularities because the function is undefined at these values and analytic in their respective neighborhoods (3:02 - 3:31).

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Видео #isolatedsingularity #definition #example #complexanalysis #mscmaths #maths #highermathematics канала Saloni Sharma