Books of Interest
Here are the names of the various books that I have at one time or
another passed around in class.
- Synge and Schild, Tensor Calculus. Good index intensive book.
- Gray, Leijnse, Kolar, and Blain, Mathematical Tools for Changing
Spatial Scales in the Analysis of Physical Systems. Horrible example
of the difficulties with vector calculus notation for integrals. All these
special cases collapse into just three theorems in differential forms.
- Schouten, Ricci Calculus. The pinnacle of index shuffling.
Look at this and weep.
- Schouten, Tensor Analysis for Physicist. The first place where
honest pictures of 1-forms and twisted 1-forms appears.
- Dava Sobel, Longitude.Nice account of the struggle to
make acceleration independent clocks, most of the problem being
bureaucrats and astronomers.
- Michael A. Penna, Richard R. Patterson, Projective Geometry and
its applications to Computer Graphics.
- Jorge Stolfi. Oriented Projective Geometry.A very clever idea,
useful for SRT aberration problems among others.
- Gerald Farin. Nurb Curves and Surfaces: from projective geometry
to practical use.
- Jan Koenderink. Solid shape.Very nice graphics.
- CTJ Dodson and T Poston.Tensor geometry.Modern tensor analysis
with lots of computer generated pictures and awful typography.
- Abrams. The Work of M.C. Escher.
- Theodore Frankel. Gravitational Curvature. One of the few
mathematics books that uses twisted differential forms.
- Jon Scieszka + Lane Smith. Math Curse. Good fun.