This third edition of Alfred Gray's famous textbook continues to offer an outstanding presentation of how to define and compute standard geometric functions along with a dialect of Mathematica for constructing new curves and surfaces from existing ones. Since Gray's death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they have reorganized the material to provide a clearer division between the text and the Mathematica code, added a Mathematica notebook as an appendix to each chapter, and addressed important new topics,...

In July 1998, I received an e-mail from Alfred Gray, telling me: " . . . I am in Bilbao and working on the second edition of Tubes . . . Tentatively, the new features of the book are: 1. Footnotes containing biographical information and portraits 2. A new chapter on mean-value theorems 3. A new appendix on plotting tubes " That September he spent a week in Valencia, participating in a workshop on Differential Geometry and its Applications. Here he gave me a copy of the last version of Tubes. It could be considered a final version. There was only one point that we thought needed to be...

The purpose of this companion volume to our text is to provide instructors (and eventu- ally students) with some additional information to ease the learning process while further documenting the implementations of Mathematica and ODE. In an ideal world this volume would not be necessary, since we have systematically worked to make the text unambiguous and directly useful, by providing in the text worked examples of every technique which is discussed at the theoretical level. However, in our teaching we have found that it is helpful to have further documentation of the various solution...

This book expresses the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Historical notes and Mathematica drawings have been added to this revised second edition.

From the reviews:

"Will do much to make Weyl's tube formula more accessible to modern readers.... A high point is the presentation of estimates for the volumes of tubes in ambient Riemannian manifolds whose curvature is bounded above or below."

--BULLETIN OF THE AMS

These materials, which have been developed and thoroughly class tested over a period of several years by the authors, are intended for use in courses in differential equations taught at the sophomore/junior level in American colleges and universities. Prerequisites for using these materials is the calculus of one variable, although calculus of several variables, and linear algrbra, are recommended. The text covers the standard topics in first and second order equations, power series solutions, first order systems, Laplace transforms, numerical methods and stability of non-linear systems. For...