Differential Geometry of Curves and Surfaces 2nd Edition by Thomas F. Banchoff (PDF)

Description

Differential Geometry of Curves and Surfaces, Second Edition takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive computer graphics applets supported by sound theory.The book explains the reasons for various definitions while the interactive applets offer motivation for certain definitions, allow students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits.New to the Second EditionReworked presentation to make it more approachableMore exercises, both introductory and advancedNew section on the application of differential geometry to cartographyAdditional investigative project ideasSignificantly reorganized material on the Gauss–Bonnet theoremTwo new sections dedicated to hyperbolic and spherical geometry as applications of intrinsic geometryA new chapter on curves and surfaces in RnSuitable for an undergraduate-level course or self-study, this self-contained textbook and online software applets provide students with a rigorous yet intuitive introduction to the field of differential geometry. The text gives a detailed introduction of definitions, theorems, and proofs and includes many types of exercises appropriate for daily or weekly assignments. The applets can be used for computer labs, in-class illustrations, exploratory exercises, or self-study aids.

User’s Reviews

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

⭐Good alternative for Do Carmo.This book is excellent readability. In addition, the book will have a description of the three-dimensional curves and surfaces other than manifolds instill a greater confidence in differential geometry to the reader.

⭐The subject matter is basically curves in two and three dimensional Euclidean space, and surfaces in three dimensional Euclidean space (There is a brief chapter on curves in n-dimensional Euclidean space, but it appears to have been added as an afterthought.) The book is obviously intended to be read before the same author’s “Differential geometry of manifolds”, and the subject is treated in a way that will facilitate the transition to the more general setting.The style of writing is clear. The book is adequately rigourous, without being pedantic. The proofs are easy to follow. There is a good selection of helpful illustrations.In the Preface the author refers readers to a website that is said to have visual material that will illustrate many of the topics discussed, but I was unable to connect to that site. It appears to be defunct. You will have to use your brain instead – which might not be a bad thing.Unfortunately, something has gone badly wrong with the Index, and the page numbers cited there bear no relation to what is in the text. That is really annoying, and I have deducted one star because of it.

⭐El libro esta muy bien. Toca todos los aspestos importantes de la geometria diferencial. Despues de cada apartado hay una buena coleccion de problemas. La pena es que ningún ejercicio de los propuestos esta resuelto. No obstante hay ejemplos resueltos por todo el libro.

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