復變函數(shù)與積分變換

內(nèi)容概要

本書是一本用于同名課程雙語教學的英文教材，編者參考多本有關的經(jīng)典原著英文教材，按照國家教育部對本課程的基本要求，結合多年的教學實踐編撰而成，內(nèi)容分兩部分，共8章，第1～6章為復變函數(shù)部分，包括complex numbers and funcfions of a complex variable（復數(shù)與復變函數(shù)），analytic functions（解析函數(shù)），complex integrals（復積分），series（級數(shù)），residues（留數(shù)），conformal mappings（保形映射），第7章和第8章是積分變換部分，包括Fourier transform（傅里葉變換）和Laplace transform（拉普拉斯變換），書中各章節(jié)都安排了足夠量的例題，在每章后也安排了大量精選的習題，并按大綱的要求及難易程度分為A、B兩類，    本書既可作為理工科大學同名課程的雙語教材，也可供有關工程技術人員參考。

書籍目錄

Chapter 1  Complex Numbers and Functions of a Complex Variable　1.1  Complex numbers and its four fundamental operations　1.2  Geometric representation of complex numbers　1.3  Complex conjugates　1.4  Powers and roots　1.5  Riemann sphere and infinity　1.6  Complex number sets　1.7  Functions of a complex variable　Exercise 1Chapter 2  Analytic Functions　2.1  The concept of analytic function　2.2  Necessary and sufficient conditions of analytic functions　2.3  Elementary functions　Exercise 2Chapter 3  Complex Integrals　 3.1  The concept of complex integral　 3.2  Cauchy integral theorem　 3.3  Cauchy integral formula　 3.4  Analytic functions and harmonic functions　 Exercise 3  Chapter 4  Series　 4.1  Series of complex numbers and series of complex functions"　 4.2  Power series　 4.3  Taylor series     4.4  Laurent series　 Exercise 4Chapter 5  Residues　 5.1  Isolated singularities　 5.2  Residues　 5.3  Application of residues in evaluating definite and improper integrals  　 Exercise 5Chapter 6  Conformal Mappings　6.1  The concept of conformal mapping　6.2  Fractional linear transformations　6.3  Condition of uniqueness　6.4  Some important fractional linear transformations　6.5  Mapping by some elementary functions　Exercise 6Chapter 7  Fourier Transform　7.1  Fourier integral and Fourier integral theorem　7.2  Fourier transform and inverse Fourier transform　7.3  Unit impulse functions　7.4  Generalized Fourier transform　7.5  The properties of Fourier transform　7.6  Convolution　Exercise 7Chapter 8  Laplace Transform　8.1  The concept of Laplace transform　8.2  The properties of Laplace transform　8.3  Inverse Laplace transform　8.4  Application of Laplace transform　Exercise 8Answers to Selected Exercises　Exercise 1　Exercise 2　Exercise 3　Exercise 4　Exercise 5　Exercise 6　Exercise 7　Exercise 8Vibliography AppendixIndex

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