references for learning about branch cuts/ branch points in complex analysis

Question

Are there any good books/online resources for learning about branch cuts at the level of introductory undergraduate complex analysis.

Thanks in advance.

score 6 · Accepted Answer · edited May 08 '11 at 05:31

6

When I was an undergrad I really enjoyed Palka's treatment of this; it is definitely accessible and rigorous.

edited May 08 '11 at 05:31

J. M. ain't a mathematician

76,540

answered May 08 '11 at 05:15

BBischof

5,967

Thank you for the recommendation. Will check it out. – Shibi Vasudevan May 08 '11 at 05:31

score 5 · Answer 2 · answered May 08 '11 at 12:09

5

See http://www.cds.caltech.edu/~nair/abel.pdf It actually doesn't require any complex analysis really, but it explains branch cuts and points for Riemann surfaces of polynomials, so it's a great introduction. It also uses these to prove an important theorem.

answered May 08 '11 at 12:09

Davidac897

4,799

Thanks a lot for the reference. – Shibi Vasudevan May 08 '11 at 16:28
Yayaya! Cool reference. +1! – BBischof May 08 '11 at 16:48
@Davidac897 this link is not working. – Nirmal Rawat Nov 08 '23 at 07:01

score 4 · Answer 3 · edited Jun 12 '20 at 10:38

I recommend to go through chapter VI: Multifunctions and chapter VII: The Logarithmic Function of Visual Complex Analysis by T. Needham.

The sections

VI.1 Example: Fractional powers, VI.2 Single-Valued Branches of a Multifunction, VI.3 Relevance to Power Series, VI.4 An Example with Two Branch Points

and

VII.1 Inverse of the Exponential Function, VII.2 The Logarithmic Power Series, VII.3 General Powers

provide a guided tour regarding branch cuts and related aspects with plenty of illuminating pictures.

references for learning about branch cuts/ branch points in complex analysis

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