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.
|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
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 .