复变函数与积分变换中的英文单词和短语解读

复变函数与积分变换Functions of ComplexVariable and IntegralTransforms第一章复数与复变函数Chapter 1 Complex Numbers and Functions of Complex Varialble复数complex number实部real number虚部imaginary unit纯虚数pure imaginary number共轭复数complex conjugate number运算operation减法subtraction乘法multiplication除法division复平面complex plane分配律distribute rule交换律exchange rule复合函数complex function复数的三角形式trigonometrical form of complexnumber模modulus辐角argument乘方power开方extraction开集open set闭集closed set邻域neighborhood充分必要条件sufficient and necessary condition 边界点boundary point有界集bounded set区域domain简单闭曲线simple closed curve连通区域connected region分段光滑piecewise smooth无穷远点point at infinity复变函数function of complex variable 单值函数single-valued function多值函数multi-valued function连续continuity不等式inequality第二章解析函数Chapter 2 Analytic Functions微分differential奇点singularity解析函数analytic function导数derivative柯西-黎曼方程Cauchy-Riemann equation 调和函数harmonic function指数函数exponential function对数函数logarithm function三角函数trigonometric function双曲函数hyperbolic function幂函数power function高阶导数higher order derivative求导法则derivation rule链式法则chain rule定义域domain导函数derivative function反函数inverse function复变函数与积分变换中的英文单词和短语第三章复变函数的积分Chapter 3 Integrals of functions of complex variable柯西积分公式Cauchy integral formula柯西不等式Cauchy inequality第四章解析函数的级数表示Chapter 4 Series Expressions of Analytic Functions复函数序列sequences of complex function级数series幂级数power series函数项级数series of functions收敛性convergence收敛半径radius of convergence泰勒级数Taylor series洛朗级数Laurent series发散divergence麦克劳林级数Maclaurin series泰勒级数展开Taylor series expansion绝对收敛absolutely convergent一致收敛uniform convergence部分和partial sum第五章留数及其应用Chapter 5 Residues and their Applications 留数residue孤立奇点isolated singularity可去奇点removable singularity本性奇点essential singularity极点polem阶极点pole of order m当且仅当if and only if亚纯函数meromorphic function第六章共形映射Chapter 6Conformal Mappings从A到B的转角oriented angle from a to b保角映射angle-preserving mapping自映射self-mapping不动点fixed point分式线性变换linear fractional transformation 多边形polygon第七章傅里叶变换Chapter 7Fourier Transforms傅里叶变换Fourier transform傅里叶积分Fourier integral卷积convolution线性性linearity对称性symmetry延迟性time shifting积分变换integral transform反演公式inversion formula共轭傅里叶积分conjugate Fourier integral广义傅里叶积分generalized Fourier integral傅里叶逆变换inverse Fourier transform傅里叶反演公式Fourier inversion formula傅里叶正弦变