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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2021

Paper 302

viii

Differentiate the identity in part vi with respect to $y^t$, multiply by $\mu_a{}^s(y)\mu_b{}^t(y)$, and use $\lambda\mu=I$. The product rule gives
$$
\boxed{
\mu_a{}^s\mu_b{}^t\frac{\partial^2z^r}{\partial y^s\partial y^t}
=\mu_a{}^s[T_b\lambda_s{}^c]\mu_c{}^r(z)
+T_b(z)\mu_a{}^r(z)}.
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 2 / viii / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 2 / viii / Solution

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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 2 / viii / Solution

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