復分析(英文影印版) [COMPLEX ANALYSIS] pdf epub mobi txt 電子書 下載 2024

圖書介紹


復分析(英文影印版) [COMPLEX ANALYSIS]


[美] 加默蘭 著



點擊這裡下載
    


想要找書就要到 求知書站
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

发表于2024-11-05

類似圖書 點擊查看全場最低價

齣版社: 世界圖書齣版公司
ISBN:9787506292290
版次:1
商品編碼:10175905
包裝:平裝
外文名稱:COMPLEX ANALYSIS
開本:24開
齣版時間:2008-05-01
用紙:膠版紙
頁數:478
正文語種:英語

復分析(英文影印版) [COMPLEX ANALYSIS] epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

相關圖書



復分析(英文影印版) [COMPLEX ANALYSIS] epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

復分析(英文影印版) [COMPLEX ANALYSIS] pdf epub mobi txt 電子書 下載 2024



具體描述

內容簡介

This book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. Students should be familiar with the Cartesian representation of complex numbers and with the algebra of complex numbers, that is, they should know that i2 = -1. A familiarity with multivariable calculus is also required, but here the fundamental ideas are reviewed. In fact, complex analysis provides a good training ground for multivariable calculus. It allows students to consolidate their understanding of parametrized curves, tangent vectors, arc length, gradients, line integrals, independence of path, and Greens theorem. The ideas surrounding independence of path are particularly difficult for students in calculus, and they are not absorbed by most students until they are seen again in other courses.

內頁插圖

目錄

Preface
Introduction
FIRST PART
Chapter 1 The Complex Plane and Elementary Functions
1.Complex Numbers
2.Polar Representation
3.Stereographic Projection
4.The Square and Square Root Functions
5.The Exponential Function
6.The Logarithm Function
7.Power Functions and Phase Factors
8.Trigonometric and Hyperbolic Functions

Chapter 2 Analytic Functions
1.Review of Basic Analysis
2.Analytic Functions
3.The CauChy-Riemann Equations
4.Inverse Mappings and the Jacobian
5.Harmonic Functions
6.Conformal Mappings
7.Fractional Linear Transformations

Chapter 3 Line Integrals and Harmonic Functions
1.Line Integrals and Greens Theorem
2.Independence of Path
3.Harmonic Conjugates
4.The Mean Value Property
5.The Maximum Principle
6.Applications to Fluid Dynamics
7.Other Applications to Physics

Chapter 4 Complex Integration and Analyticity
1.Complex Line Integrals
2.Fundamental Theorem of Calculus for Analytic Functions
3.Cauchys Theorem
4.The Cauchy Integral Formula
5.Liouvilles Theorem
6.Moreras Theorem
7.Goursats Theorem
8.Complex Notation and Pompeius Formula

Chapter 5 Power Series
1.Infinite Series
2.Sequences and Series of Functions
3.Power Series
4.Power Series Expansion of an Analytic Function
5.Power Series Expansion at Infinity
6.Manipulation of Power Series
7.The Zeros of an Analytic Function
8.Analytic Continuation

Chapter 6 Laurent Series and Isolated Singularities
1.The Laurent Decomposition
2.Isolated Singularities of an Analytic Function
3.Isolated Singularity at Infinity
4.Partial Fractions Decomposition
5.Periodic Functions
6.Fourier Series

Chapter 7 The Residue Calculus
1.The Residue Theorem
2.Integrals Featuring Rational Functions
3.Integrals of Trigonometric Functions
4.Integrands with Branch Points
5.Fractional Residues
6.Principal Values
7.Jordans Lemma
8.Exterior Domains

SECOND PART
Chapter 8 The Logarithmic Integral
1.The Argument Principle
2.Rouches Theorem
3.Hurwitzs Theorem
4.Open Mapping and Inverse Function Theorems
5.Critical Points
6.Winding Numbers
……
THIRD PART
Hints and Solutions for Selected Exercises
References
List of Symbols
Index

前言/序言

  This book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. Students should be familiar with the Cartesian representation of complex numbers and with the algebra of complex numbers, that is, they should know that i2=-1. A familiarity with multivariable calculus is also required, but here the fundamental ideas are reviewed. In fact, complex analysis provides a good training ground for multivariable calculus.It allows students to consolidate their understanding of parametrized curves, tangent vectors, arc length,gradients, line integrals, independence of path, and Greens theorem. The ideas surrounding independence of path are particularly difficult for students in calculus, and they are not absorbed by most students until they are seen again in other courses.
  The book consists of sixteen chapters, which are divided into three parts.The first part, Chapters I-VII, includes basic material covered in all undergraduate courses. With the exception of a few sections, this material is much the same as that covered in Cauchys lectures, except that the emphasis on viewing functions as mappings reflects Riemanns influence. The second part, Chapters VIII-XI, bridges the nineteenth and the twentieth centuries. About half this material would be covered in a typical undergraduate course, depending upon the taste and pace of the instructor. The material on the Poisson integral is of interest to electrical engineers, while the material on hyperbolic geometry is of interest to pure mathematicians and also to high school mathematics teachers. The third part, Chapters XII-XVI, consists of a careful selection of special topics that illustrate the scope and power of complex analysis methods. These topics include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The final five chapters serve also to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis.

復分析(英文影印版) [COMPLEX ANALYSIS] 下載 mobi epub pdf txt 電子書
復分析(英文影印版) [COMPLEX ANALYSIS] pdf epub mobi txt 電子書 下載
想要找書就要到 求知書站
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

用戶評價

評分

joly

評分

還可以的啊還可以的啊

評分

joly

評分

還行

評分

joly

評分

下學期學習的工具書,價格有點貴

評分

joly

評分

還行

評分

質量很好,服務很到位!

類似圖書 點擊查看全場最低價

復分析(英文影印版) [COMPLEX ANALYSIS] pdf epub mobi txt 電子書 下載





相關圖書


本站所有內容均為互聯網搜索引擎提供的公開搜索信息,本站不存儲任何數據與內容,任何內容與數據均與本站無關,如有需要請聯繫相關搜索引擎包括但不限於百度google,bing,sogou

友情鏈接

© 2024 tushu.tinynews.org All Rights Reserved. 求知書站 版权所有