INTRODUCTION TO ANALYSIS WITH COMPLEX NUMBERS

類似書籍推薦給您

This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series. The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head. The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.

Real and complex analysis (3版)

類似書籍推薦給您

【簡介】 Description This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. 【目錄】 Table of Contents Chapter 1: Abstract Integration Chapter 2: Positive Borel Measures Chapter 3: Lp-Spaces Chapter 4: Elementary Hilbert Space Theory Chapter 5: Examples of Banach Space Techniques Chapter 6: Complex Measures Chapter 7: Differentiation Chapter 8: Integration on Product Spaces Chapter 9: Fourier Transforms Chapter 10: Elementary Properties of Holomorphic Functions Chapter 11: Harmonic Functions Chapter 12: The Maximum Modulus Principle Chapter 13: Approximation by Rational Functions Chapter 14: Conformal Mapping Chapter 15: Zeros of Holomorphic Functions Chapter 16: Analytic Continuation Chapter 17: Hp-Spaces Chapter 18: Elementary Theory of Banach Algebras Chapter 19: Holomorphic Fourier Transforms Chapter 20: Uniform Approximation by Polynomials

A Friendly Approach to Complex Analysis (2版)

類似書籍推薦給您

The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text. The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained. Request Inspection Copy Sample Chapter(s) Overview Chapter 1: Complex numbers and their geometry Contents: Complex Numbers and Their Geometry Complex Differentiability Cauchy Integral Theorem Taylor and Laurent Series Harmonic Functions Solutions to All Exercises Readership: Undergraduate students in complex analysis.