## 伯克利资格考试与口试:PDE

Sample Questions from Past Qualifying Exams

This list may give the impression that the exams consist of a series of questions fired at the student one after another. In fact most exams have more the character of a conversation with considerable give and take. Hence this list cannot be expected to indicate accurately the difficulties involved.

The list indicates the professor associated to each question where available. Some have been in the MGSA files for a while, and this information has been lost (if it was ever there).

The listing by section is approximate, since some questions may fit under more than one heading.

## 伯克利资格考试与口试:几何

Sample Questions from Past Qualifying Exams This list may give the impression that the exams consist of a series of questions fired at the student one after another. In fact most exams have more the character of a conversation with considerable give and take. Hence this list cannot be expected to indicate accurately the difficulties involved.

The list indicates the professor associated to each question where available. Some have been in the MGSA files for a while, and this information has been lost (if it was ever there).

The listing by section is approximate, since some questions may fit under more than one heading.

## 别再怀疑自己的意志力

$\newcommand{\rd}{\mathrm{d}}\newcommand{\set}{\left\{#1\right\}}\newcommand{\Lp}{\Delta\,}$事实上, 假设$\rd s^2=g_{ij}\rd x^i\rd x^j$是$M^2=(\Omega,g)$上的Riemann度量. 要使$M^2$ 是共形平坦的, 那么
$\rd s^2=g^{ij}\rd x_i\rd x_j=e^{2\lambda u}\left((\rd x_1)^2+(\rd x_2)^2\right).$