REAL & COMPLEX ANALYSIS 3E (5P) (Int'l Ed) (TMHE IE OVERRUNS) Paperback – 16 Mar. 1987

* PhysicalIt has 416 pages of good quality paper and ink and physically sound binding.* Target audience, H.N.D, Undergraduate, Post GraduateIt's required to understand undergraduate math, to postgraduate studies. These are targeted so that the earlier chapters require a bedrock of '...advanced calculus, settheoretic manipulations, metric spaces, continuity and convergence...' page xiii, and this is found in the first ... 'seven chapters of Rodins book 'Principles of Mathematical Analysis', page xiii . I have most of these from different book sources.* What's in it then?(1) Abstract Integration (2) Positive Borel Measures, (3) L p Spaces, (4) Elementary Hibert Space Theory (5) Examples of Banach Space Techniques, (6) Complex Measures, (7) Differentiation, (8) Integration on Product Spaces, (9) Fourier Transforms, (10) Elementary Properties of Holomorphic Functions, (11) Harmonic Functions (12) the Maximum Modulus Principle, (13) Approximation by Rational Functions, (14) Conformal Mapping, (15) Zeros of Holomorphic Functions (16) Analytic Continuation, (17) H p Spaces, (18) Elementary Theory of Banach Algebras, (19) Holomorphic Fourier Transforms, (20) Uniform Approximation by Polynomials, Appendix, Notes and Comments, Bibliography, List of Special Symbols, Index.* What's the best bits then?This book '...contains a first-year graduate course in which basic techniques and theorems of analysis are presented in such a way that intimate connections between various branches are strongly emphasised.' Preface page xiii. (at the top)The essential keys to unlocking analysis here are repeated many times and in many different areas that you find the theory is made clear this way. If you read the first 15 chapters, - which takes some doing - then you can choose a few from the remaining chapters. I have broken the difficulties of this book but I still need to go over and over these chapters.It's tough going and needs to be reread over and over to get it in your head. You may skip one obscure sentence that defines a mathematical operation that holds you back from grasping this whole chapter, so it's better not to skip going forward and back. Its not the most open and explaining book I have read on analysis of both real and complex forms, but it still chugs along. The legendary questions are tough if you're not aware of the level it's pitched at. I found rereading 'Engineering Mathematics' Stroud, any edition, helped to sculpt the practical questions as on top of the theoretical aspects.* SummaryIf your not aware, you can get this book second - hand, with mine having a discoloured by sunlight spine. Mine was a lot cheaper to buy this way. It's a demanding book that fights with you to what it explains and how it's fleshed out.

I am a fan of Rudin's books. This one "Real and Complex Analysis" has served as a standard textbook in the first graduate course in analysis at lots of universities in the US, and around the world.The book is divided in the two main parts, real and complex analysis. But in addition, it contains a good amount of functional and harmonic analysis; and a little operator theory.I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.Some of the exercises are notoriously hard, but I think that is good: It simply means that they serve as work-projects when the students use the book. And this approach probably is more pedagogical as well.After surviving some of the hard exercises in Rudin's Real and Complex, I think we learn things that stay with us for life; you will be "marked for life!"Review by Palle Jorgensen, December 2004.

Overrated