 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 332

For the surface $F(x,z,t)=z-\zeta(x,t)=0$, an outward <normal vector> and positively oriented <tangent vector> are
$$
\boxed{
\hat{\mathbf n}
=\frac{(-\zeta_x,1)}{\sqrt{1+\zeta_x^2}}},
\qquad
\boxed{
\hat{\mathbf t}
=\frac{(1,\zeta_x)}{\sqrt{1+\zeta_x^2}}}.
$$
With $\zeta=\epsilon e^{ikx}$ and $|k\epsilon|\ll1$, <linearization> gives
$$
\boxed{
\hat{\mathbf n}=(-ik\epsilon e^{ikx},1)+O(\epsilon^2k^2)},
\qquad
\boxed{
\hat{\mathbf t}=(1,ik\epsilon e^{ikx})+O(\epsilon^2k^2)}.
$$

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 332 / 4 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 332 / 4 / b / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 332 / 4 / b / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)