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Elementary Differential Geometry, 2nd  무료배송

 
지은이 : Pressley, Andrew
출판사 : Springer-Verlag
판수 : 2판
페이지수 : 487
ISBN : 9781848828902
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
     

 

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum ?nothing beyond first courses in linear algebra and multivariable calculus ?and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. 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: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com

From the reviews of the second edition 밒 am very happy to report that the new edition of Pressley뭩 Elementary Differential Geometry is an even better book than the first edition ?. full solutions to all problems given in an appendix. ?Most of the problems are in the book and have solutions in the back. ?The upshot is that this is still an excellent book and still my first choice for an undergraduate introduction to differential geometry.?(Fernando Q. Gouv?, The Mathematical Association of America, May, 2010)


 

1. Curves in the plane and in space.
2. How much does a curve curve?.
3. Global properties of curves.
4. Surfaces in three dimensions.
5. Examples of surfaces.
6. The first fundamental form.
7. Curvature of surfaces.
8. Gaussian, mean and principal curvatures.
9. Geodesics.
10. Gauss?theorema egregium.
11. Hyperbolic geometry.
12. Minimal surfaces.
13. The Gauss Bonnet theorem.
A0. Inner product spaces and self adjoint linear maps.
A1. Isometries of euclidean spaces.
A2. M�bius transformations.
Hints to selected exercises.
Solutions
Index

"Pressley's gives you a very comprehensible and down to earth introduction to differential geometry.
By avoiding the more modern and abstract generalizations of differential geometry to more than three dimensions you really feel that you grasp what the theorems and methods are about. In this way you are able to work your way quickly through the book and avoid getting stuck and loosing interest. Another plus is that the book contains lots of examples and fully worked answers to all exercises, which makes it perfect for self-study.
The downside is that the book is not as exhuastive as you perhaps would like, when you have looked at books like O'Neills and DoCarmos ... on the other hand, you only need to spend a fraction of the time to get through Pressleys.
I definitely think that this is a much better book that Struiks classical work (by being more structured and goal oriented) and an excellent introduction to further studies in differential and Riemann geometry."


"I have purchased hundreds of technical books and really treasure the ones that seem to have been written in order to really convey the material rather than impress the reader with how smart the author is. This is such a book. The material is remarkably clear and the author's style strikes me as a notable example of the mathematical writing styles put forth in the articles comprising the text "How to Write Mathematics." For example, the material proceeds in a logical chain such that the reader is never confronted with a term or concept before it has been explained. The notation is defined meticulously and repeatedly so the reader is not forced to continually refer backwards through the text to remember the meaning of the symbols. This also is a boon for "grasshopper readers" who will use the text as a reference, as opposed to a linear reader. Symbols don't change meaning, are not overloaded, and seem to have been chosen for intuitive appeal. For example, a lower-case gamma denotes a parametric function for a curve and, to me, the shape of the gamma suggests the sorts of curves being discussed. In my experience, this book is best in class."
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