8
$\begingroup$

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

Thanks in advance.

$\endgroup$
0
5
$\begingroup$

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

$\endgroup$
1
  • $\begingroup$ Thank you for the recommendation. Will check it out. $\endgroup$ – Shibi Vasudevan May 8 '11 at 5:31
5
$\begingroup$

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.

$\endgroup$
2
  • $\begingroup$ Thanks a lot for the reference. $\endgroup$ – Shibi Vasudevan May 8 '11 at 16:28
  • $\begingroup$ Yayaya! Cool reference. +1! $\endgroup$ – BBischof May 8 '11 at 16:48
3
+50
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.