Modern Differential Geometry of Curves and Surfaces with Mathematica® (Textbooks in Mathematics) 3rd Edition by Alfred Gray (PDF)

Description

Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using 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 reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions.The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

User’s Reviews

Editorial Reviews: Review “This is a nicely readable textbook on differential geometry. It offers an outstanding, comprehensive presentation of both theoretical and computational aspects … There are hundreds of illustrations that help the reader visualize the concepts. … It is a nicely written book, strongly recommended to all with an interest in differential geometry, its computational aspects and related fields.” ― In EMS Newsletter, June 2007

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I take one star off because the “Look inside” facility is deceptive. It shows coloured pictures while the actual book features black /white only. Not a big deal but…As for the shipping etc, all was fine.

⭐I have purchased the third edition of Modern Differential Geometry of Curves and Surfaces with Mathematica.I have seen the second edition before and I think that second edition is better than the third edition.If you plan to buy this book and I could give you an advice: I would say buy the second edition.The second edition has some chapters, Mathematica algorithms and appendices, which are not in the third.Eu comprei a terceira edição do livro “Modern Differential Geometry of Curves and Surfaces with Mathematica”.Eu vi a segunda edição antes e penso que a segunda está melhor que a terceira.Se você planeja comprar este livro eu poderia dar-lhe um conselho: diria para comprar a segunda edição.A segunda edição tem alguns capítulos, algoritmos do Mathematica e appendices que não estão na terceira edição.

⭐The quality of book delivered was perfect.

⭐Excellent reference text book

⭐The contents of this tome is encompassing. Everything you need to read the current publications can be found in this tome.One quibble: the MATHEMATICA notebooks are not conveniently available. I, at least, have to copy the code by hand (fingertip). Since the code is not very long (thanks to MATHEMATICA’s powerful routines), this is not a severe burden.The treatment of non-Euclidean geometry is wonderfully presented and optimal for students of General Relativity.

⭐I own the paper textbook as well as the kindle version. I’m really satisfied with the contents of the volume and I use it frequently. Unfortunately in the textbook from page 810 to 841 page numbers and the titles and numbers of definitions, propositions, theorems and so on are missing. In the kindle version the footnotes and some pictures are missing. The Mathematica coding examples are outdated, but can be adapted to the latest Mathematica version (nevertheless, a good exercise). I am looking forward to a newer, updated version of the book.

⭐Beau et “gros” livre de géométrie différentielle, très complet, appliqué à Mathematica (avec des Notebooks Mathematica à télécharger séparément sur le net…). Le niveau d’anglais requis ne pose aucun problème particulier et la partie mathématique est relativement bien expliquée tout au long du livre. Je recommande donc ce bouquin sans hésiter !À noter que le livre (la 3e édition que j’ai reçu en tout cas !) est relié, et que les figures à l’intérieur sont en couleur, ce qui peut sans doute justifier son prix, un peu élevé tout de même !Nice book for differential geometry

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