|Visual Complex Analysis
22nd December 2013
The complex analysis is long considered a valuable tool for physicists and engineers alike. The textbooks available on complex analysis provide adequate mathematical background for students. But the presentation is usually geared more towards the application side of the business. As a result there is always this element of doubt in reader's mind that even though the complex analysis is extensively used in physics, is it just a mathematical abstraction or is there a correlation to the nature which is not obvious to most of us.
The Visual Complex Analysis written by Tristan Needham and published by Oxford University Press, is an extraordinary hard to put down book. Author has taken great care in explaining the topics so as to build a thought sequence from chapter one to the final chapter. The historical perspective is provided but it is not stand-alone and integrates very well with the course material. There are plenty of innovative examples presented visually, but the strength of the book really lies in its precise language. The arguments are very clear and reader is sure to understand the logic being developed step-by-step along with some really neat graphics.
The chapter on the Möbius transformations is a sheer pleasure to go through. It is extremely well-written and by the time the intricacies of inversion and reflection are discussed, the reader is already shaking his head in wonder. Similarly the chapters on Non-Euclidean Geometry, Winding Numbers and Topology, Physics and Topology, Complex Integration and Flows and Harmonic Functions are great reads.
A background in basic complex analysis probably will be useful before studying VCA, though not necessary. It is a must-have classic for anyone who takes physics seriously. The books we will be discussing, are the books which have made a difference for us non-experts. Visual Complex Analysis is definitely one such book and it is highly recommended.