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

Thanks in advance.

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    Thank you for pointing this out. I have rectified this somewhat.2011-05-08

3 Answers 3

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

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    Thank you for the recommendation. Will check it out.2011-05-08
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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.

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    Yayaya! Cool reference. +1!2011-05-08
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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.