Hello World

Welcome to Hexo! This is your very first post. Check documentation for more info. If you get any problems when using Hexo, you can find the answer in troubleshooting or you can ask me on GitHub.

Quick Start

Create a new post

1	$ hexo new "My New Post"

More info: Writing

Run server

1	$ hexo server

More info: Server

Generate static files

1	$ hexo generate

More info: Generating

Deploy to remote sites

1	$ hexo deploy

More info: Deployment

公式示例

设函数 $f(x,y)$ 的全微分为 $df(x,y)=(2ax+by)dx+(2by+ax)dy$ ,( $a$ , $b$ 为常数),且 $f(0,0)=-3,f_{x}^{'}(1,1)=3$ ,求 $f(x,y)$

本题给的是全微分,但是可以看成两个偏微分,并且较为基础,所以放在第一题

\frac{∂f}{∂x}=2ax+by,\frac{∂f}{∂y}=2by+ax

直接对两个偏微分求不定积分,可以得到原函数.注意对x积分时,将y看作常数,因此最后的 $+C$ 实际上应该写作 $+g(y)$

f(x,y)=ax^{2}+bxy+g(y)=by^{2}+axy+h(x)

显然两者是同一个函数,因此对应的项的系数也相同,即 $a=b$ ,对x求偏导,得到 $f_{x}^{'}(1,1)=2a+b=3$ ,故 $f(x,y)=x^2+xy+y^2-3$