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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2019

Paper 2

Integrating the equation through $t=1$ gives the <jump condition for an impulse>
$$
T_1(1^+)-T_1(1^-)=-1.
$$
For $1<t<2$ the equation is again homogeneous, so propagation of the post-jump temperature gives
$$
T_1(t)-T_\infty=(\Delta e^{-a}-1)e^{-a(t-1)}
=(\Delta-e^a)e^{-at}.
$$
Therefore
$$
\boxed{T_1(t)=T_\infty+(T_0-T_\infty-e^a)e^{-at}}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 7C / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 7C / b / Solution

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Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 7C / b / Solution

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