Notes by Robert T Jantzen
too ambitious for an undergraduate level course, but a useful reference
if you find these notes useful please contact me! See later notes and an undergraduate textbook online.
0 | Introduction | 1 |
1 | Linear Algebra Summary (metrics, antisymmetrization, duals) | 1 |
2 | Some more explanation for 1 (some examples) | 19 |
3 | Still more explanation for 1 (more on antisymetrization, metric index shifting, duals) | 28 |
4 | The end of linear algebra (more on wedge, metric dual) | 36 |
5 | Differential geometry on Rn using Cartesian coordinates | 43 |
6 | Examples of differential manifolds, coordinate transformations | 52 |
7 | The exterior derivative | 63 |
8 | Orientation, integration of p-forms, normals, volume elements (glitch on inner/outer orientation) | 71 |
9 | Stokes' theorem without metric, with metric | 92 |
10 | Covariant differentiation, parallel transport | 102 |
11 | Gauge fields, covariant exterior derivative* | 119 |
12 | Lie derivative, Lie dragging | 132 |
These were scanned into PDF directly using a Canon photocopier, not quite so
nice quality.
Here is a comparison test with the HP scanner scanning into Adobe Acrobat:
Canon versus HP.
* on the first page of this section there is an unfortunate ambiguity of
symbols, but easily distinguished since they have consistent index positioning:
the two contravariant indexed omega is the
dual frame basis 2-form ωij =
ωi
\wedge
ωj ,
the 1 contravariant, 1 covariant indexed omega is the connection 1 -form matrix ωi j
.