Needham, Chapter 11, 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. Divergence and curl of several vector fields (PDF)
2. Flux and work of x^2 and i(1/r^2)e^{i theta} (PDF)
3. Flux and work of 1/[z sin(z)]
   • (i) C centred at -Pi (PDF)
   • (ii) C centred at 0 (PDF)
   • (iii) C centred at Pi (PDF)
   • (iv) C centred at 2Pi (PDF)
   • (v) Rectangle (PDF)
4. Flux and work of z csc(z)
   • (i) C centred at -Pi (PDF)
   • (ii) C centred at 0 (PDF)
5. Integral of f(z) = z e^{iz} (PDF)
6. Braden's Theorem (PDF)
7. Braden's Theorem applied (PDF)
8. Omega of (2n+1) sources at +/- n Pi (PDF)
9. Derivative of potential of sources at +/- n Pi (PDF)
10. Rotation of C(z conjugate) (PDF) with animation file (Quicktime movie, AVI)
11. Omega = w + exp(w) (PDF)
12. Omega = (1/2)(exp(z)+1)/(exp(z)-1) (PDF)
13. Dipole inserted into continuous flow (PDF)
14. Pole and sink inserted into continuous flow at 1 and -1 (PDF). Animated .gif file of flow for Exercise 14. To view, save to disc and open in browser. (GIF)
15. Flow from sources and sinks on square w. circle streamline (PDF)
16. Two vortices make Cassinian curve (PDF)
17. Cassinian streamlines and potentials of quadrupole (PDF)

1. Section I (PDF)
2. Section II (PDF)
3. Section III (PDF)
4. Streamlines (PDF)

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