math 520 differentiable manifolds
prof. ghrist ; fall 2004
new! advice and
pseudo-problems for final!
homework assignments
- assignment 1 : due 9/8 :
mht,
pdf
- assignment 2 : due 9/17 :
mht,
pdf
- assignment 3 : due 9/24 :
mht
- assignment 4 : due 9/31 :
mht,
pdf
- assignment 5 : due 10/8 :
mht
- assignment 6 : due 10/25 :
mht, pdf
- assignment 7 : due 11/8 :
mht,
pdf
- assignment 8 : due 11/17 :
mht,
pdf
- assignment 9 : due ad kalendas
graecas :
mht,
pdf
lecture notes
- lecture 1 : manifolds :
mht,
pdf
- lecture 2 : examples :
mht,
pdf
- lecture 3 : smooth maps :
mht,
pdf
- lecture 4 : approximations :
mht
- lecture 5 : tangent vectors :
mht
- lecture 6 : derivatives :
mht
- lecture 7 : bundles :
mht
- lecture 8 : sections :
mht
- lecture 9 : flows :
mht
- lecture 10 : vector fields and flows :
mht
- lecture 11 : Lie derivatives of vector fields :
mht
- lecture 12 : flows and Lie derivatives :
mht
- lecture 13 : the Inverse Function
Theorem : mht
- lecture 14 : the Implicit Function
Theorem : mht
- lecture 15 : intro to foliations :
mht
- lecture 16 : more foliations :
mht
- lecture 17 : involutivity :
mht
- lecture 18 : the Frobenius Theorem :
mht
- lecture 19 : bundle basics :
mht
- lecture 20 : pullbacks and morphisms :
mht
- lecture 21 : tubular neighborhoods /
transversality :
mht
- lecture 22 : the Thom theorem and
applications :
mht
- lecture 23 : intro to linear forms :
mht,
pdf
- lecture 24 : linear forms and form
fields : mht,
pdf
- lecture 25 : wedges, exterior derivative :
mht,
pdf
- lecture 26 : pullbacks and contractions :
mht,
pdf
- lecture 27 : the Cartan formula :
mht,
pdf
- lecture 28 : intro to de Rham cohomology :
mht,
pdf
- lecture 29 : the Poincare Lemma :
mht,
pdf
- lecture 30 : integration I :
mht,
pdf
- lecture 31 : integration II :
mht,
pdf
- lecture 32 : Stokes' Theorem :
mht,
pdf
- lecture 33 : applications of Stokes' :
mht,
pdf
- lecture 34 : connections on bundles :
mht,
pdf
- lecture 35 : parallel transport;
geodesics : mht,
pdf
- lecture 36 : curvature of a connection :
mht,
pdf
- lecture 37 : introduction to Riemannian
geometry : mht,
pdf