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  • Modern Differential Geometry of Curves and Surfaces with Mathematica (Textbooks in Mathematics)

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Modern Differential Geometry of Curves and Surfaces with Mathematica (Textbooks in Mathematics)

4.1 out of 5 stars (17)

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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.

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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

About the Author

Abbena, Elsa; Salamon, Simon; Gray, Alfred

Product details

  • Publisher ‏ : ‎ Chapman and Hall/CRC
  • Publication date ‏ : ‎ June 21, 2006
  • Edition ‏ : ‎ 3rd
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 1016 pages
  • ISBN-10 ‏ : ‎ 1584884487
  • ISBN-13 ‏ : ‎ 978-1584884484
  • Item Weight ‏ : ‎ 10.6 ounces
  • Dimensions ‏ : ‎ 7 x 2.25 x 10 inches
  • Part of series ‏ : ‎ Textbooks in Mathematics
  • Best Sellers Rank: #3,177,950 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.1 out of 5 stars (17)

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Alfred Gray
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4.1 out of 5 stars
17 global ratings
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Top reviews from the United States

  • 5 out of 5 stars
    Five Stars
    Reviewed in the United States on April 6, 2018
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    The quality of book delivered was perfect.

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  • 4 out of 5 stars
    Excellent book, but updated only for Mathematica 5.2 in 2006
    Reviewed in the United States on August 3, 2026
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    This is an excellent book with advanced concepts of Differential Geometry explained and demonstrated with examples of Mathematica code and Notebooks throughout. Since the book dates from 2006 the code and Notebooks were updated only to Mathematica version 5.2 (i.e. now 10 versions old). Wolfram AI can help in locating and translating the Notebooks (they are only now available through the WayBack Machine). There are newer built-in functions (and downloadable ResourceFunction code) in Mathematica version 15 which fill some gaps in Mathematica 5.2, however the extra understanding gained by deriving from scratch (often Symbolically) is of huge benefit. The book is laid out with coursework, particularly appropriate for students, but is also a very useful reference for those with dulled memories and sudden tricky problems. Thus as expected this is a mixture of an advanced textbook with a comprehensive hands-on library of worked examples.

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  • 4 out of 5 stars
    Incredibly beautiful introduction differential geometry. Mathematica version very dated.
    Reviewed in the United States on March 9, 2023
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    This is a classic and excellent first book to study differential geometry. The power of Mathematica and visualization of the geometry is obvious with the first few pages. Unfortunately a lot of the code for Mathematica has changed since this version of the book was written. An updated version of the text with downloadable code is badly needed. Fortunately the Mathematica home version is available for self learners at home. I fortunately have have it through my teaching position. This is a excellent book for a initial study of differential geometry. It is also a beautiful way to appreciate the beauty of Mathematica. Hopefully the book can be updated.

    2 people found this helpful
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  • 3 out of 5 stars
    Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition
    Reviewed in the United States on September 29, 2009
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    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.

    20 people found this helpful
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  • 1 out of 5 stars
    Buyer Beware: Mathematica code is obsolete and notebook files are not available
    Reviewed in the United States on September 5, 2024
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    This book was published in 2006 (3rd edition) and written for a previous version of Mathematica, now long obsolete. According to the book's editor, the Mathematica code is "entirely nonfunctional," and the electronic notebook files are no longer available, despite the representation in the Preface that they are available from the publisher's website.

    Since the potential value of the book is largely in its Mathematica code, this is disappointing. The publisher further confirms there are no plans for a fourth edition.

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  • 4 out of 5 stars
    Reseña
    Reviewed in the United States on August 28, 2019
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    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.

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  • 5 out of 5 stars
    Excellent !!
    Reviewed in France on December 18, 2020
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    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 !

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  • 5 out of 5 stars
    A classic: yet not in any way outdated
    Reviewed in Germany on September 30, 2020
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    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.

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  • 4 out of 5 stars
    Ofrece una información clara y con muchos ejemplos
    Reviewed in Spain on February 9, 2024
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    Lamentablemente, los autores sobrevivientes (el Dr. Gray ya no está con nosotros) han abandonado el libro. Me explico: en las primeras ediciones se ofrecía un material adicional que contiene las soluciones de muchos problemas, en forma de Notebooks de Mathematica™. Este material es muy importante, al extremo que después de cada capítulo del libro se muestra una referencia al Notebook correspondiente; ese Notebook contiene información deliberadamente oculta en el libro. Pues bien, los Notebooks ya no están disponibles en la página web de la editorial. Puesto en contacto con la Editorial, me han notificado que los autores ya no actualizan la página en que se ofrecía originalmente el material. Esto es, el enlace que figura en el libro no funciona, y ni siquiera se ofrecen los Notebooks originales (que podrían servir como base para versiones actualizadas). Esto es un problema grave.

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  • 5 out of 5 stars
    研究論文に最適。
    Reviewed in Japan on January 4, 2013
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    学会での論文発表の基礎資料として活用しました。とても理解しやすかったです。

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  • 5 out of 5 stars
    Excellent reference text book
    Reviewed in the United Kingdom on November 12, 2018
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    Excellent reference text book

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