Visual Complex Analysis
"Visual Complex Analysisis a delight, and a book after my own heart.  By his innovative and exclusive use of the geometrical  perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis." --Roger Penrose"Tristan Needham'sVisual Complex Analysiswill show you the field of complex analysis in a way you almost certainly have not seen before.  Drawing on historical sources and adding his own insights, Needham develops the subject from the ground up, drawing us attractive pictures at every step of the way.  If you have time for a year course, full of fascinating detours, this is the perfect text; by picking and choosing, you could use it for a variety of shorter courses.  I am tempted to hide the book from my own students, in order to appear more clever for popping up with crisp historical anecdotes, great exercises, and pictures that explain things like that mysterious 2*pithat crops up in integrals.  Whether you useVisual Complex Analysisas a text, a resource, or entertaining summer reading, I highly recommend it for your bookshelf."--American Mathematical Monthly"Delivers what its title promises, and more: an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas. . .A truly unusual and notably creative look at a classical subject." --American Mathematical Monthly"One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But to replace our rich visual intuition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's 'Visual Complex Analysis' with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices--but his are interesting." --New Scientist"Committed to the exclusive use of geometrical arguments and content to pay the price of 'an initial lack of rigour', he has produced a radically new text.  The author writes "as though [he] were explaining the ideas directly to a friend".  This informal style is excellently judged and works extremely well."--Mathematical Review"This is a book in which the author has been willing to make himself available as our teacher.  His own voice enters in a rather charming way....I recommendVisual Complex Analysis, as something to read and enjoy, to share with students, and perhaps to inspire other books in which the voice of the author is vividly present to teach and explain."--American Mathematical Monthly