Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability / 6 / b / ii

Table of contents
- Solution ii

Solution

For the spatial mode with eigenvalue

κ_{n} = (nπ / L)^{2}

, the temporal ordinary differential equation is

T_{n}^{'} + D (\frac{nπ}{L})^{2} T_{n} = 0.

Its general solution is

T_{n} (t) = C_{n} exp (- \frac{D n ^{2} π ^{2}}{L ^{2}} t), C_{n} \in R .

The printed reference to “each solution

X (x)

... in part (b)” refers to (b)(i). The zero spatial mode gives

u = 0

irrespective of

T

and contributes no additional nonzero solution.^[ref]

 Ancestors (12)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version