راهنمای کامل حل مسائل تحلیل واقعی و پیچیده

This is a complete solution guide to all exercises from Chapters 1 to 20 in Rudin's Real and Complex Analysis . The features of this book are as follows: It covers all the 397 exercises from Chapters 1 to 20 with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied. There are 40 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems. Sections in each chapter are added so as to increase the readability of the exercises. Different colors are used frequently in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only) Necessary lemmas with proofs are provided because some questions require additional mathematical concepts which are not covered by Rudin. Many useful or relevant references are provided to some questions for your future research. Cover Author Preface List of Figures Contents Abstract Integration Positive Borel Measures Lp-Spaces Elementary Hilbert Space Theory Examples of Banach Space Techniques Complex Measures Differentiation Integration on Product Spaces Fourier Transforms Elementary Properties of Holomorphic Functions Harmonic Functions The Maximum Modulus Principle Approximations by Rational Functions Conformal Mapping Zeros of Holomorphic Functions Analytic Continuation Hp-Spaces Elementary Theory of Banach Algebras Holomorphic Fourier Transforms Uniform Approximation by Polynomials Index Index Bibliography