Needham, Chapter 7, Visual Complex Analysis—PDF files with notes, figures, and some answers for exercises
The figures in this list pertain to Visual Complex Analysis (1997) by Tristan Needham. The illustrations pertain to suggested exercises in the text, to exercises at ends of chapters, and to ideas suggested by the text. In a some cases, they are attempts to reproduce figures found in the text. See also the animated demos. Both the figures and demos are plotted with Mathematica 10.
Some answers to exercises are provided without figures. The answers are my own and they are not endorsed by the author of Visual Complex Analysis. The answers in the archives of Vasco are in general more consistent and reliable. I have consulted them frequently in my own studies. Current discussions of the book and the exercises appear on Vasco's forum.
- Winding numbers (PDF)
- Preimages of loops (PDF)
- p-points and winding numbers of three functions (PDF)
- Cubic on expanding circle, Pt (i) (PDF), Pt (ii-iv) Explain the crimp, Inellipse touches midpoints of triangle (PDF), Pt (v) Show that critical points are foci (PDF)
- Jacobian and eigenvalues (PDF)
- Eigenvalues and multiplicity (PDF)
- Multiplicity of non-analytic f (PDF)
- Nyquist Stability Criterion (PDF)
- Nyquist Stability Criterion example (PDF)
- Rouche's Theorem I (PDF)
- Rouche's Theorem II (PDF)
- Rouche's Theorem generalized (PDF)
- Derivative winds (PDF)
- Winding on a continuous but odd function (PDF)
- Brouwer's (PDF)
- Odd number roots (PDF)
- Root in sphere (PDF)
- Direction xi f'(p) for max |f(p)| (PDF)
- Pits and saddles in modular surfaces (PDF)
- Show f = g throughout interior (PDF)
- P-points and poles on Gamma (PDF)
- Prove argument principle (PDF)
