Needham, Chapter 10, 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.

1. Ch.10, Ex. 1. Circular streamlines of vector field z^2 (PDF)
2. Ch.10, Ex. 2. Plot of 1/(z sin^2(z)) (PDF)
3. Ch.10, Ex. 3. Factorize polynomial by inspection of plot (PDF)
4. Ch.10, Ex. 4. Simple closed loop streamline must contain singular point (PDF)
5. Ch.10, Ex. 5,6. Indices of singular points, and Sectors of vector fields (PDF)
6. Ch.10, Ex. 5,6. Indices of singular points, and Sectors of vector fields (PDF)
7. Ch.10, Ex. 7. Prasolov's problem (PDF)
8. Ch.10, Ex. 8. Fixed points on sphere (PDF)
9. Ch.10, Ex. 9. Fixed points on sphere, cont. (PDF)
10. Ch.10, Ex. 10. Investigate limitation on plotting types of singular behavior on sphere UNDER CONSTRUCTION ()
11. Ch.10, Ex. 11. Area of polygon on sphere and Legendre's argument. (PDF)
12. Ch.10, Ex. 12. Poincare-Hopf and Euler characteristic on sphere and torus. (PDF)
13. Ch.10, Ex. 13. Poincare-Hopf applied to gravity field. (PDF)

1. Ch. 10, Notes (PDF)

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