Modern Mathematics and Physics, Spring 1984

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.

Table of Contents [about 150 8.5x11in US sized paper sheets]

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 ω^ij = ωⁱ \wedge ω^j ,
the 1 contravariant, 1 covariant indexed omega is the connection 1 -form matrix ωⁱ _{j
.}