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## Prerequisite material from 18.100

Rudin, *Principles of mathematical analysis*, ch 9:
Inverse and implicit function theorems

Rudin, *Principles of mathematical analysis*, ch 11:
Fatou's lemma; dominated convergence theorem

## Prerequisite material from 18.034

Birkhoff-Rota, *Ordinary differential equations*, ch 6:
Existence and uniqueness theorems for ODEs

## Reference for lecture Fri 9 Sep

Munkres, *Analysis on manifolds*, sections 21-22:
Volume of a parallelotope; volume of a parametrized submanifold

## References for lecture Mon 3 Oct

HM notes: The conserved quantity for geodesics of a certain family of metrics

Klingenberg, *Riemannian geometry*, section 3.5:
Geodesics of a triaxial ellipsoid

## Reference for lecture Fri 7 Oct

Morgan, *Riemannian geometry: A beginner's guide*, ch 7:
Geodesics of Schwarzschild space; precession of Mercury