ps1sol

# And b figure 4 serial of maps from exterior of the

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -plane that g (w) maps one-to-one to the whole z -plane. c) Describe and attempt to draw a Riemann surface on which f (z ) is single-valued and to which g (w) maps one-to-one. Comment on the misleading nature of your picture. d) Identify the branch points of f (z ) and introduce a branch cut to make f (z ) singlevalued. Solution 7 a) z 3 = |z | 3 ei( 1 1 Arg(z ) + 2πk 3 3 ), k = 0, 1, 2 (42) So, f (z ) = z 3 has three values for z = 0. 1 7 ¡£¡¡£¡¡£¡ ¤¤¤ £¤¡¡¡¡¡¡ ¤¡¡£¤¡¡£¤¡¡£¤ ££ £ £ ¡£¤¡¡£¤¡¡£¤¡ ¤¡¤¡¤¡¤¡¤¡¤¡¤ £¡¤¡£¡¤¡£¡¤¡£ ¡£¡¤¡£¡¤¡£¡¤ £¤¡¡£¤£¡¡£¤£¡¡£¤£ £ ¤£ ¤£ ¤£ ¤¤¡¤¡¤¡¤¡¤¡¤¡¤ £¡£¡¡£¡¡£¡ ¡¡£¤£¡¡£¤£¡¡£¤£ ¡¦¡¡¦¡¦¡¥ ¥¥¥¥¥ ¡¦¡¡¦¡¦¡ ¦¦¡¡¦¦¡¡¡¦¦¥¡¥ ¦¡¡¦¡¡¡¦¡¥¥ ¡¦¡¡¦¡¦¡¥¡ ¥¥ ¦¥¥ ¥¥ ¦¥¥ ¦¥¥ ¥¥¥¥¥¥ ¦¦¡¡¦¦¡¡¡¦¦¡¥ ¥¡¦¥¡¥¡¦¥¡¦¥¡¡ ¦¡¡¦¡¡¡¦¡¥¥ ¥¡¥¡¥¡¥¡¥¡ ¡¦¡¡¦¡¦¡¥¥ ¨¡¨¡¨¡¨¡¨¡¨¡¡¨¡¨¡¡¨¡¨¡¨¡ §¡¨¡¨¡¨¡¨¡¨¡¡¨¡¨¡¡¨¡¨¡¨¡ §§§§§ §§ §§§ ¡§¡§¡§¡§¡§¡¨¡§¡§¡¨¡§¡§¡§¡¨ §¨¡¨¡¨¡¨¡¨¡¨¡§¡¨¡¨¡§¡¨¡¨¡¨¡§ ¨¡¡¡¡¡¡¨§¨¡¡¡¨§¨¡¡¡¡¨§¨ ¨§ ¨§§ ¨§§ ¨§§ ¨§§ ¨§§ ¨§§ ¨§§ ¨§§ ¨§§ ¨§§ §¡¨¡¨¡¨¡¨¡¨¡§¡¨¡¨¡§¡¨¡¨¡¨¡§ ¨¡§¡§¡§¡§¡§¡¨§¡§¡§¡¨§¡§¡§¡§¡¨§ ¨¡¡¡¡¡¡§¨¡¡¡§¨¡¡¡¡§¨ §§¡§¡§¡§¡§¡§¡¡§§¡¡§¡§¡§¡ ¡§¨¡§¨¡§¨¡§¨¡§¨...
View Full Document

## This note was uploaded on 02/22/2010 for the course ACM 95A taught by Professor Nilesa.pierce during the Fall '06 term at Caltech.

Ask a homework question - tutors are online