1、復(fù)變函數(shù)與積分變換functions of complexvariable and integraltransforms第一章復(fù)數(shù)與復(fù)變函數(shù)chapter 1 complex numbers and functions of complex varialble復(fù)數(shù) complex number實(shí)部 real number虛部imaginary unit純虛數(shù) pure imaginary number共軛復(fù)數(shù) complex conjugate number運(yùn)算 operation減法 subtraction乘法 multiplication除法 division復(fù)平面complex plan

2、e分配律distribute rule交換律 exchange rule復(fù)合函數(shù) complex function復(fù)數(shù)的三角形式trigonometrical form of complexnumber模 modulus輻角 argument乘方 power開方 extraction開集 open set閉集 closed set鄰域 neighborhood充分必要條件 sufficient and necessary condition&界bo boundary point有界集 bounded set區(qū)域 domain簡(jiǎn)單閉曲線 simple closed curve連通區(qū)域co

3、nnected region分段光滑piecewise smooth無(wú)窮遠(yuǎn)點(diǎn)point at infinity復(fù)變函數(shù)function of complex variable 單值函數(shù) single-valued function連續(xù) continuity不等式 inequality第二章解析函數(shù)chapter 2 analytic functions微分 differential奇點(diǎn) singularity解析函數(shù) analytic function導(dǎo)數(shù) derivative柯西-黎曼方程 cauchy-riemann equation調(diào)和函數(shù) harmonic function指數(shù)函數(shù)ex

4、ponential function對(duì)數(shù)函數(shù)logarithm function三角函數(shù)trigonometric function雙曲函數(shù)hyperbolic function冪函數(shù)power function高階導(dǎo)數(shù)higher order derivative求導(dǎo)法則derivation rule鏈?zhǔn)椒▌tchain rule定義域domain導(dǎo)函數(shù)derivative function反函數(shù)inverse function復(fù)變函數(shù)與積分變換中的英文單詞和短語(yǔ) 第三章復(fù)變函數(shù)的積分chapter 3 integrals of functions of complex variable柯西積

5、分公式 cauchy integral formula柯西不等式cauchy inequality第四章解析函數(shù)的級(jí)數(shù)表示chapter 4 series expressions of analytic functions復(fù)函數(shù)序列sequences of complex function級(jí)數(shù) series冪級(jí)數(shù)power series函數(shù)項(xiàng)級(jí)數(shù)series of functions收斂性convergence收斂半徑radius of convergence泰勒級(jí)數(shù)taylor series洛朗級(jí)數(shù)laurent series發(fā)散 divergence麥克勞林級(jí)數(shù)maclaurin seri

6、es泰勒級(jí)數(shù)展開taylor series expansion絕對(duì)收斂absolutely convergent一致收斂uniform convergence部分和 partial sum第五章留數(shù)及其應(yīng)用 chapter 5 residues and their applications!數(shù) residue孤立奇點(diǎn)isolated singularity可去奇點(diǎn)removable singularity本性奇點(diǎn)essential singularity極點(diǎn) polem 階極點(diǎn)pole of order m當(dāng)且僅當(dāng)if and only if亞純函數(shù)meromorphic function第六

7、章共形映射 chapter 6conformal mappings從 a 到 b 的轉(zhuǎn)角 oriented angle from a to b保角映射 angle-preserving mapping自映射self-mapping不動(dòng)點(diǎn) fixed point分式線性變換linear fractional transformation 多邊形polygon第七章傅里葉變換chapter 7fourier transforms傅里葉變換fourier transform傅里葉積分fourier integral卷積 convolution線性性linearity對(duì)稱性symmetry延遲性time shifting積分變換integral transform反演公式inversion formula共軛傅里葉積分conjugate fourier integral廣義傅里葉積分generalized fourier integral傅里葉逆變換inverse fourier transform傅里葉反演公式fourier inversion formula傅里葉正弦變