# !!> EPUB ❄ Visual Complex Analysis ✿ Autor Tristan Needham – Andy-palmer.co.uk

I first read this book in 2001 I have now re read it and I hope to re read it many times This is an exceptional book and I am dumbfounded by how illuminating it has been with a second read 11 years later The author makes a distinct effort to provide deep principally geometric insights into complex analysis as well as connections between complex analysis and non Euclidean geometry as well as physics The power of visualization and the amplitwist concept is clear I still need to re read this book to get the most out of it but the explorations of conformal mappings analyticity harmonic functions from the multiple viewpoints was a unique and deeply rewarding experience.See the website This Radical First Course On Complex Analysis Brings A Beautiful And Powerful Subject To Life By Consistently Using Geometry Not Calculation As The Means Of Explanation Aimed At Undergraduate Students In Mathematics, Physics, And Engineering, The Book S Intuitive Explanations, Lack Of Advanced Prerequisites, And Consciously User Friendly Prose Style Will Help Students To Master The Subject Readily Than Was Previously Possible The Key To This Is The Book S Use Of New Geometric Arguments In Place Of The Standard Calculational Ones These Geometric Arguments Are Communicated With The Aid Of Hundreds Of Diagrams Of A Standard Seldom Encountered In Mathematical Works A New Approach To A Classical Topic, This Work Will Be Of Interest To Students In Mathematics, Physics, And Engineering, As Well As To Professionals In These Fields I have held off on writing a review on this book for some time now After having read it completely, and, importantly, having worked with complex variables extensively, I am finally ready to deliver a verdict on it.I applaud the author s effort to visually describe the complex plane in particularly complex multiplication and integration He also goes into great detail on Mobius transformations and other geometric concepts However, I think that he missed the opportunity to describe complex differentials completely While he speaks of analytic functions being everywhere aplitwist, he doesn t describe the nature of differentials at analytic points namely, the differential remains the same, regardless of which path we take from the point This much clearly explains the rigidity of analytic functions along with theorems like FTC, maximum modulus, etc which follow directly from this rigidity.I believe that he forsakes his own thesis in describing the argument principle in generic topological arguments These arguments are far involved than they need to be.More than anything, I dislike how he uses results that haven t been proved It is quite annoying to use Cauchy s Theorem throughout the book, not proving it till very late.All that said, this is an overall great book that will get you thinking about the concepts His writing style is very skillful, and, obviously, he provides a lot of figures to help get his point across It is definitely worth adding to your library, but I think that you will need at least one other text to completely grasp the subject I personally recommend Gamelin s book. Complex analysis can challenge the intuition of the new student This text is unique, among high quality textbooks, in giving a careful and thorough exploration of the geometric meaning underlying the usual algebra and calculus of complex numbers The Cauchy Riemann equations define what is meant by a holomorphic function Restricting to these particularly pleasant and useful functions, the formalism of calculus looks very much like ordinary calculus Too many students muddle through complex analysis with the notion that it looks like calculus, except some extra nice functions also hold Such students commonly become competent, but they seldom actually get good at complex analysis In particular, for many engineers, complex calculus remains an unpalatable mystery, even though they know how to do the calculations That is the difficulty, and Needham corrects the whole of the difficulty perfectly.Ahlfors is a great classical text Conway two volumes is thorough, clear, and modern Carrier, Krook, and Pearson is especially concise and well oriented to the practical calculations of engineering and applied science Berenstein Gay is very modern and oriented to a very high quality undergraduate or beginning graduate who intends to continue in very pure mathematics All these and e.g Saff are at least very good or perhaps excellent texts Because there is a body of problems that beginners are expected to be able to work mathematics is also a culture there are expectations , it is probably necessary to pick one of these texts and to use Needham s book as one of two texts for an excellent course I know of no other book that gives the great intuitive and geometric understanding of complex analysis that Needham gives I would, under no circumstances, teach any beginning course in complex analysis at any school anywhere at any time for any reason without using Needham as one of the texts If I were feeling particularly self satisfied, I might possibly use it as the only text I myself seldom feel so confident Perhaps you do This text is used frequently at M.I.T and at Oxford That seems to me a great recommendation The book is very well and clearly written The prose flows It is a great joy to read. The two stars are not for the book, which is a masterpiece of exposition It s a brilliant introduction to this topic, creating an intuitive feel for its methods and ideas through provocative geometric arguments My low rating is for the kindle version those wonderful geometric arguments are made wonderful by helpful and ingenious diagrams, many of which don t get reproduced in the digital version Without the figures to guide a reader, the exposition is compromised when he refers to diagram X and you can t see diagram X, what follows is hard to read Save the money and buy the print version And then get ready for Needham to blow your mind You ll never see Calculus Analysis the same way again. I LOVE the printed, paper copy, it is absolutely among the best math book I ve ever studied Been waiting for a Kindle version for a long time But the electronic version is of a low quality, it can not display pages properly, feels like a xeroxed copy of the original book