# 复分析作业代写Complex analysis代考

## 代写复分析作业代写Complex analysis

### 全纯函数Holomorphic function代写

• 柯西-黎曼方程Cauchy–Riemann equations
• 指数函数Exponential function
• 皮卡定理 Picard theorem

## 复分析的历史

Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Important mathematicians associated with complex numbers include Euler, Gauss, Riemann, Cauchy, Weierstrass, and many more in the 20th century. Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number theory. In modern times, it has become very popular through a new boost from complex dynamics and the pictures of fractals produced by iterating holomorphic functions. Another important application of complex analysis is in string theory which examines conformal invariants in quantum field theory.

## 复分析课后作业代写

For such restricted paths, ${ }^{5}$ we define
(1) the integral of $f$ on $\gamma$ with respect to arc-length
$$\int_{\gamma} f(z)|d z|=\int_{0}^{1} f(\gamma(t))\left|\gamma^{\prime}(t)\right| d t$$
(2) the path $\gamma$ traversed backward
$$\gamma_{-}(t)=\gamma(1-t), \quad \text { for all } t \in[0,1],$$
and
(3) the length of the curve $\gamma$
$$L(\gamma)=\text { length of } \gamma=\int_{\gamma}|d z|$$