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復(fù)變函數(shù)與積分變換 版權(quán)信息
- ISBN：9787030193513
- 條形碼：9787030193513 ; 978-7-03-019351-3
- 裝幀：一般膠版紙
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>>
復(fù)變函數(shù)與積分變換 本書特色
本書是哈爾濱工業(yè)大學(xué)復(fù)變函數(shù)與積分變換雙語教材，具有課件，適合于雙語教學(xué)。是學(xué)習(xí)復(fù)變函數(shù)與積分變換的有利工具書，配合主教材使用效果更佳。 以“雙語化、分層次、立體化”為特點(diǎn)，融中英文雙語、分層次紙質(zhì)化教材，同步學(xué)習(xí)輔導(dǎo)，中、英文版教學(xué)課件、電子教案以及習(xí)題詳解于一體的創(chuàng)新型系列化教材，適應(yīng)普通高等教育不同層次學(xué)校學(xué)生學(xué)習(xí)使用.
復(fù)變函數(shù)與積分變換 內(nèi)容簡介
本書是一本用于同名課程雙語教學(xué)的英文教材，編者參考多本有關(guān)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(jié)合多年的教學(xué)實踐編撰而成，內(nèi)容分兩部分，共8章，第1～6章為復(fù)變函數(shù)部分，包括complex numbers and functions of a complex variable（復(fù)數(shù)與復(fù)變函數(shù)），analytic functions（解析函數(shù)），complex integrals（復(fù)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(xí)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(xué)同名課程的雙語教材，也可供有關(guān)工程技術(shù)人員參考。
復(fù)變函數(shù)與積分變換 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 1
chapter 2 analytic functions
2.1 the concept of analytic function
2.2 necessary and sufficient conditions of analytic functions
2.3 elementary functions
exercise 2
chapter 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 4
chapter 5 residues
5.1 isolated singularities
5.2 residues
5.3 application of residues in evaluating definite and improper integrals
exercise 5
chapter 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 6
chapter 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 7
chapter 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 8
answers to selected exercises
exercise 1
exercise 2
exercise 3
exercise 4
exercise 5
exercise 6
exercise 7
exercise 8
bibliography
appendix
index
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 1
chapter 2 analytic functions
2.1 the concept of analytic function
2.2 necessary and sufficient conditions of analytic functions
2.3 elementary functions
exercise 2
chapter 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 4
chapter 5 residues
5.1 isolated singularities
5.2 residues
5.3 application of residues in evaluating definite and improper integrals
exercise 5
chapter 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 6
chapter 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 7
chapter 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 8
answers to selected exercises
exercise 1
exercise 2
exercise 3
exercise 4
exercise 5
exercise 6
exercise 7
exercise 8
bibliography
appendix
index
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復(fù)變函數(shù)與積分變換 作者簡介
蓋云英，女，教授，博士生指導(dǎo)教師，教學(xué)帶頭人；哈爾濱工業(yè)大學(xué)理學(xué)院數(shù)學(xué)系教授，現(xiàn)在已經(jīng)退休，原來為哈爾濱工業(yè)大學(xué)復(fù)變函數(shù)與積分變換學(xué)科帶頭人。四十年教齡教師，教學(xué)經(jīng)驗豐富，出版暢銷經(jīng)典教材三部。
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