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# 解析学

## はじめに

高校で微分を習ったときは

$$
\frac{dy}{dx} \tag{1}
$$

は$$dy$$を$$dx$$で割ったものではない、と教わったかもしれないが、ここから先は紛れもなく「$$dy$$を$$dx$$で割ったものである」と理解していないと何度もつまずくことになる。大学に入って全微分の式

$$
dz = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy
$$

を解析学で習うだろうから$$dz$$や$$dx$$という「なにか」が存在することは知っているだろう。では (1) 式に現れる$$dx$$や$$dy$$と全微分はどういった関係があるか説明できるだろうか。

多様体論にまつわる書籍は微分、偏微分、全微分といった概念をしっかりと理解してイメージできるようになっているとスムーズに読み進めることができるだろう。

## 微分

## 全微分と偏微分


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