Elementary Differential Geometry: Curves and Surfaces. Edition Martin Raussen. DEPARTMENT OF MATHEMATICAL SCIENCES, AALBORG. The Differential Geometry in the title of this book is the study of the geometry of curves .. Andrew Pressley, Elementary Differential Geometry: Second Edition,. 1 . PDF | These notes are for a beginning graduate level course in differential geometry. It is assumed that this is the students' first course in the.
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Elementary Differential Geometry presents the main results in the differential ISBN ; Digitally watermarked, DRM-free; Included format: PDF. Andrew Pressley - Elementary Differential Geometry - Edition 1 - Ebook download as PDF File .pdf) or read book online. Andrew Pressley - Elementary. This book is an elementary account of the geometry of curves and surfaces. It is written for students who have completed standard courses in calculus and linear .
download eBook. download Softcover. FAQ Policy. About this Textbook Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. New features of this revised and expanded second edition include: The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: Around additional exercises, and a full solutions manual for instructors, available via www.
Show all. Table of contents 13 chapters Table of contents 13 chapters Curves in the plane and in space Pressley, Andrew Pages How much does a curve curve? Pressley, Andrew Pages Global properties of curves Pressley, Andrew Pages Surfaces in three dimensions Pressley, Andrew Pages Examples of surfaces Pressley, Andrew Pages All that is needed is some familiarity with linear algebra and vector calculus, but even this book is self contained enough that even without exposure to either of those it is still approachable.
I think that after working through this book a student will be well prepared to take on a more advanced book like Riemannian Geometry by do Carmo or Differential Geometry by Kuhnel.
Perfect introduction to the field of differential geometry. I found this book to be exactly what I needed to build my fundamental knowledge of the subject, especially in terms of computations. Very accessible for undergrads. I've used both books together and felt that the two books compliment each other very well. What O'Neill's book lacks in set-up and motivation, McCleary's book more than makes up for. What McCleary's book lacks in computational methodology and rigour, O'Neill's book more than makes up for.
If you're feeling passionate about getting into the subject of differential geometry and modern geometry in general, I cannot highly recommend using both books together enough. This book is not like new, but very new.
The package is very, very good! Thank you!
An excellent intro to diffy geo. I enjoyed this course in college.
The book was difficult in areas, but I think it covers the subject area well. One person found this helpful. Schoenagel Top Contributor: Quantum Physics. I have long desired to write a review of this textbook.
I began to write a review three separate times, I never finished. Each time I felt that my review had fallen short.
This attempt will hardly be different: However, in order to set things in motion, I extract this line from the review of the website of Mathematical Association of America: Now, that line from that mostly positive MAA review pertains to the second edition.
If a student for whom this text is addressed preface: If an instructor is unable to successfully "teach" a course utilizing this textbook, I am at a loss, as the text is a hallmark of erudition! Let us take a closer look into this beautiful textbook as it is not a treatise nor a monograph: What you learn in earlier chapters is placed into service again, at increasing levels of abstraction.
If you do not care for that methodology, seek another source. Thus, the initial chapter leads up to the inverse-function theorem page 39, stated without proof. Exercises 10 and 11 taken as a set will first ask you to supply a proof, then will ask for a computation one to one, onto, inverse. A summary concludes chapter one. Learn why "the geometry of Euclidean space can be derived from the dot-product. Parametrization, orientation, these are emphasized. Covariant derivative introduced.
Regards frame fields: Next, connection one-forms and structure equations. Revisit vector fields encountered second chapter. You revisit parametrization "in first importance in practical computations.
Jacobian matrix, this will be utilized time and time again. Linear Independence, much utilized pages 45, , We shall follow the order of topics in chapter one. There you have it. Now, review chapter one, because chapter four is a continuation, of sorts. Chapter one introduced one-forms, chapter two used them for the structure equations. Now, in an additional three sections, we will learn of "forms on a surface.
A dose of topology page precedes a dose concerning manifolds page A summary concludes the chapter. How does one improve upon this exposition?
Chapter five revisits "shapes" shape-operator , here for surfaces. A spiral approach! Gaussian curvature and determinant page The chapter concludes with a nice section of surfaces of revolution pages Cartan's frames chapter two will be called upon for the answer.
Isometries met in the third chapter will be revisited: Recall one to one, onto, inverse function theorem we utilized those in chapter four. I highlight an excellent discussion of integration and orientation you met that once in chapter four. Surfaces of revolution, you get it again page ! We free ourselves from the geometry of Euclidean-three-space. We generalize the "dot-product.
Geodesics, we generalize straight lines. Recall, the triangle-inequality page Here, bottom of page Conclusion of chapter seven is an introduction to Gauss-Bonnet theorem: A summary concludes the chapter, as it does every chapter and, every chapter begins with an introductory survey of things to come.
I have not included everything I wanted to include, there is too much of efficacy. The textbook is well-written, introductory and fairly modern. Answers to the odd-numbered exercises are included. An answer booklet exists for the even-numbered exercises which I have. Hints are provided for many others. The exercises are so well-written and so clearly-enunciated, that with a study of the text there seems but few reasons that each and every exercise can not be completed with the utmost confidence in your result.
By the way: No tensors, no Christoffel symbols for that, examine the introductory text of Kreyszig. By the way, this is a mathematics textbook, so very little physics is given any mention. By remaining focused upon mathematics, Barrett O'Neill has offered a beautiful exposition. A first-rate exposition which every mathematics and physics student third-year should study!
See all 17 reviews. site Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more about site Giveaway. This item: Elementary Differential Geometry, Revised 2nd Edition. Set up a giveaway. Customers who viewed this item also viewed. Kristopher Tapp.