Complex Analysis for Mathematics and Engineering, 5/e
暫譯: 數學與工程的複變分析，第5版

John H. Mathews, Russell W. Howell

Complex Analysis for Mathematics and Engineering, 5/e

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Revised and updated, the new Fifth Edition of Complex Analysis for Mathematics and Engineering presents a comprehensive, student-friendly introduction to Complex Analysis.  Its clear, concise writing style and numerous applications make the foundations of the subject matter easily accessible for students and proofs are presented at an elementary level that is understood by students with a sophomore calculus background.  Believing that mathematicians, engineers, and scientists should be exposed to a careful presentation of mathematics, attention to topics such as ensuring required assumptions are met before the use of a theorem or algebraic operations are applied.  A new chapter on Z-Transforms and Applications provides students with a current look at Digital Filter Design and Signal Process.

 

Table of Contents

Chapter 1:   Complex Numbers
Chapter 2:   Complex Functions
Chapter 3:   Analytic and Harmonic Functions
Chapter 4:   Sequences, Julia and Mandelbrot Sets, and Power Series
Chapter 5:   Elementary Functions
Chapter 6:   Complex Integration
Chapter 7:   Taylor and Lauret Series
Chapter 8:   Residue Theory
Chapter 9:   Z-Transforms and Applications
Chapter 10:  Conformal Maping
Chapter 11:  Applications of Harmonic Functions
Chapter 12:  Fourier Series and the Laplace Transform

 

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經過修訂和更新，新的第五版《數學與工程的複變分析》提供了一個全面且適合學生的複變分析入門。其清晰、簡潔的寫作風格和眾多應用使得該主題的基礎對學生來說易於理解，證明以初級水平呈現，適合具有大二微積分背景的學生。相信數學家、工程師和科學家應該接觸到數學的仔細呈現，特別注意在使用定理或進行代數運算之前，確保所需假設已滿足。新增的Z變換及其應用章節為學生提供了有關數位濾波器設計和信號處理的最新視角。



 


目錄



第1章：複數
第2章：複函數
第3章：解析函數與調和函數
第4章：序列、朱利亞集與曼德布羅特集、冪級數
第5章：初等函數
第6章：複積分
第7章：泰勒級數與洛朗級數
第8章：留數理論
第9章：Z變換及其應用
第10章：保形映射
第11章：調和函數的應用
第12章：傅立葉級數與拉普拉斯變換



 

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