Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to $G$-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective.
The Woman and the Car is a faithfully reproduced, quirky classic from the dawn of motoring - and quirky testament to womankind's perennial claim on the steering wheel! Take a spin through a time - 1909, to be precise - when no right-thinking lady would consider solo motoring without her revolver, and when the installation of a secret compartment for powder-puff was de rigeur. In the vintage driver's seat of this 'chatty little handbook' is record-breaking Edwardian motoriste Dorothy Levitt, exhorting the budding 'lady driver' to approach the newfangled contraption without fear and reassuring those who believed it was 'impossible to look anything but hideous when in an automobile.'
Every card has a special job to do. Long Card eats lots of cake and sings lots of songs as a ...birthday card! Wide Card travels all round the world as a ...postcard! But what will Little Card's job be? Here's a clue...There's a very special place (full of books) that might just be perfect for a card his size...As long as he can whisper! Quirky and adorable, this tale of a little card who gives it all he's got is complete with an unexpected twist and a surprise, joyful ending.
One service mathematic;., has Jcndcml the 'Et moi, .. ~ si j'avait su comment CD revcnir, human race. It has put COIDDlOJI SCIISC back je n'y scrais point allC.' whc:rc it belongs, on the topmost shell next Jules Verne to the dusty canister labc1lcd 'dilcardcd nOD- The series is divergent; tbcre(on: we may be sense'. Eric T. Bcll able to do something with it o. Hcavisidc Mathematics is a tool for thought. A highly necessary tooll in a world where both feedbaclt and nonÂ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other paJts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered comÂ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
This is the author's debut collection of sentimental of poetry and short stories that are written based upon real-life experiences and some fictional situations. These poems and stories address love, friendships, families, comical situations, and the natural world. Pictures (mostly taken by the author, others used with permission) are scenic moments captured in South Carolina, Tennessee, and Hawaii.
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