by bob jantzen, Department of Mathematics and
Statistics, Villanova University

with initial typesetting help from Hans Kuo, Taiwan [2007]

: dgn.pdf**current book PDF**

[**now all crosslinks work in the PDF!**]

Fall 2017: an independent study not using this book awakened interest in it again, so some editing changes are in the works.

(version: Feb 1, 2015, it has grown to about 750 pages plus 50 some pages in an incomplete solution manual [now I am working on that], about 10 MB altogether)

Spring 2013 MAT5600 over, editing stopped for summer travel [see summarizing notes and taped lectures at this web site]

- table of contents and preface [200K]
- chapter 0 on index notation in matrix form for up to 2 index objects

Original handwritten notes for
undergraduate Differential Geometry class Spring 1991.

Serendipitously typeset
and expanded by bob for Spring 2008 class.

bob taught this course in Spring 2013,
with special relativity incorporated into the mathematical examples and
exercises and symmetry groups into the text and exercises.

**News.**

Working on the problems and problem solutions. Stalled again.

**History.**

LaTeX conversion **done** 2007-2008 with the tremendous help from Hans Kuo,
without which this book would never exist. Raw latex and first pass
polishing edit done while adding more concrete examples used in actually teaching
the course Spring 2008. Rereading from start to finish needed to round out what has
been done so far. .

Stalled by research and teaching and life since June 2008

Reader correction November 25, 2008 [after memory stick crashed with a few latest changes made in Rome Summer 2008, then had to reconstruct them!]

Minor correction February 2009 [typo in problem 1.2.2 on p16, thanks, Chris! anybody else out there who can help proof this stuff?]

February 2010. Reorganization of all the section textfiles into chapter and appendix files. A student is doing an independent study so I am rereading the book slowly.

Kepler problem updated October 2011.Fall 2012. Getting ready for teaching this in Spring 2013, adding applications to relativity. Extensive editing in progress Fall 2012. The missing thread on symmetry groups is being woven into the text in various chapters.

Spring semester 2013 (thanks to Cole Johnston VU '14 for pushing me to offer
this course), constant editing while teaching from the book. big push
spring break the first week of March. Added:
Appendix A.3 on
curves in space and surface (and spacetime!) to review multivariable calculus. Appendix
A.4 on surfaces in
space (and spacetime) to review multivariable calculus.
New special relativity Appendix A.2 after hyperbolic geometry appendix A.1, with a
problem on the Frenet-Serret geometry of a timelike helix in 3-d spacetime in
appendix A.3, to
introduce immediately students to actual special relativity mathematics based
only on their multivariable calculus background.

Black hole
embedding diagram and parallel transport along symmetry circles leading to the
GP-B geodetic gyro precession developed to motivate the course. Geodesic
deviation discussion illustrated by nearby meridians on surfaces of revolution,
and geodesics nearby extremal parallels.

April 2013. Eduard Bachmakov (VU '14) helps fix hyperref package to make PDF active hyperlinks, etc. Thanks, Eduard!

Fall 2013 And finally bob solves the equation cross-referencing to worked problems, giving each exercise a brief name.

Winter 2014 bob adds some problems dealing with the curvature and geodesic deviation on an ellipsoid of revolution, thanks to Charles Karney, an expert on geodesics on spheroidal models of the Earth.

March 2014 bob adds a section on the geodesics of the Schwarzschild black hole equatorial plane 3d Minkowski spacetime, and circular orbits (helices in the spacetime, comparable to the Lorentz helix in appendix C.

Figure scans of hand drawn figures (temporary?) These need to be replaced either by better hand drawn figures for now, or maple output when possible.

- dgnfigps.zip

.ps figure scan files: scan0001-scan0032 (part 1), scan0040-scan0115 (part 2) - dgnfigjpg.zip

.jpg figure scan files: scan0001-scan0032 (part 1), scan0040-scan0115 (part 2) [for windows previewing thumbnails]

LaTeX files

- dgn.tex LaTeX main file [dgntexfiles]

Figure drawing files (no longer used):

- dgnfigdrp.zip LaTeX picture environment
coding (no longer necessary, incorporated into latex chapter files)

[limited, circles not of arbitrary radius, so PicTeX preferrable in some cases] - dgnfigmp.zip metapost coding to produce eps output (no longer necessary)
- Maple plot exports [this seems to be the easiest solution for me, but the filesize
is way to big in the Maple EPS output]:

[dgnepsfiles.zip, dgnepsfiles2013.zip]

Maple 11-17 .mw files [still to clean up]:

**Geodesics on the Torus and other Surfaces of Revolution
Clarified Using
Undergraduate Physics Tricks with Bonus:
Nonrelativistic and Relativistic Kepler
Problems
**(in progress Fall 2009)

**Why not extend this to a screw-rotation symmetric helical tube, the shape
of cavatappi pasta?**

**General Relativity, Cosmology and Pasta?
a life of USA-Italy academic commuting** (Talk April 2012)

"Geodesics on Surfaces with Helical Symmetry: Cavatappi Geometry," (2012).