dr bob's elementary differential geometry

a slightly different approach based on elementary undergraduate linear algebra, multivariable calculus and differential equations

There are lots of books on differential geometry, including at the introductory level. Why yet another one by an author who doesn't seem to take himself that seriously and occasionally refers to himself in the third person? This one is a bit different than all the rest. dr bob loves this stuff, but how to teach it to students at his own (not elite) university in order to have a little more fun at work than usual? This unique approach may not work for everyone, but it attempts to explain the nuts and bolts of how a few basically simple ideas taken seriously underlie the whole mess of formulas and concepts, without worrying about technicalities which only serve to put off students at the first pass through this scenery. It is also presented with an eye towards being able to understand the key concepts needed for the mathematical side of modern physical theories, while still providing the tools that underlie the classical theory of surfaces in space. Examples of curves and surfaces in 2- and 3-dimensional spacetimes will be incorporated as examples, with an Appendix presenting a review of the elementary special relativity (hyperbolic geometry, directly analogous to trigonometry) needed to make sense of them.

on-line book site