复变函数教程 - staff.ustc.edu.cnstaff.ustc.edu.cn/~jwguo/teaching/complexA/fang.pdf · 2.3...
Transcript of 复变函数教程 - staff.ustc.edu.cnstaff.ustc.edu.cn/~jwguo/teaching/complexA/fang.pdf · 2.3...
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[General Information]书名=复变函数教程作者=方企勤页数=325SS号=10236932出版日期=1996年12月第1版
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封面页书名页版权页前言页目录页第一章 复数与复空间 1 复数域 2 复数的表示 3 复数的运算 4 不等式 5 圆周和直线方程 6 关于圆周的对称点 7 复数的球面表示与扩充复平面 习题第二章 复平面的拓扑 1 复平面上的开集与闭集 2 完备性 3 紧性 4 曲线 5 连通性 6 连续函数 习题第三章 解析函数概念与初等解析函数 1 解析函数概念 2 可导的充要条件 3 导数的运算 4 导数的几何意义与函数的实可微 5 指数函数 6 儒可夫斯基函数 7 分式线性变换 8 三角函数 9 对数函数 10 幂函数 11 儒可夫斯基函数的反函数与反三角函数 11.1 儒可夫斯基函数的反函数 11.1 反三角函数 习题第四章 Cauchy定理与Cauchy公式 1 积分 2 Cauchy定理 3 Cauchy公式 4 变上限积分确定的函数 5 最大模原理与Schwarz引理 习题第五章 解析函数的级数展开 1 函数项级数 1.1 数项级数 1.2 函数项级数与Welerstrass定理 1.3 级数?的收敛性 2 幂级数与Taylor展式 2.1 幂级数 2.2 解析函数的Taylor展式
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2.3 零点的孤立性与唯一性 3 Laurent 级数与Laurent展式 3.1 Laurent 级数 3.2 Laurent 展式 3.3 孤立奇点 4 整函数与亚纯函数 习题第六章 留数定理和幅角原理 1 留数定理 1.1 留数的定义与计算 1.2 留数定理 2 幅角原理与Rouché定理 2.1 关于零点与极点的一般定理 2.2 幅角原理与Rouché定理 3 求解析函数的零点数 4 单叶解析函数的性质 5 求亚纯函数的展式 6 求某些函数的定积分 习题第七章 调和函数 1 共轭调和微分与Green公式 1.1 调和微分与共轭调和微分 1.2 Green公式 2 平均值性质 3 Poisson公式与Poisson积分 3.1 Poisson公式 3.2 Poisson积分 4 几个等价命题与Harnack原理 4.1 调和函数的几个等价命题 4.2 Harnack原理 5 次(下)调和函数 6 Dirichlet问题 习题第八章 解析开拓 1 解析开拓概念与幂级数解析开拓 1.1 解析开拓概念 1.2 幂级数的解析开拓 2 对称原理 3 单值性定理 3.1 沿曲线的解析开拓 3.2 单值性定理 习题第九章 共形映射 1 共形映射的例子 1.1 单连通区域情形 1.2 二连通区域性形 2 黎曼存在定理 2.1 Montel定理 2.2 黎曼存在定理 3 边界对应 3.1 函数?(w)的连续开拓 3.2 函数f(z)的连结开拓
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4 多角形的共形映射 4.1 Schwarz-Chrlstoffel公式 4.2 矩形情形 习题附录习题答案与提示名词索引参考书目附录页