18.950 - Differential Geometry (Fall 2016)

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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