First Steps in Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook First Steps in Differential Geometry write by Andrew McInerney. This book was released on 2013-07-09. First Steps in Differential Geometry available in PDF, EPUB and Kindle. Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
First Steps in Differential Geometry
First Steps in Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook First Steps in Differential Geometry write by Andrew McInerney. This book was released on 2015-08-05. First Steps in Differential Geometry available in PDF, EPUB and Kindle. Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
Elementary Differential Geometry
Elementary Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Differential Geometry write by A.N. Pressley. This book was released on 2010-03-10. Elementary Differential Geometry available in PDF, EPUB and Kindle. 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 ul
Introduction to Differential Geometry
Introduction to Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Differential Geometry write by Joel W. Robbin. This book was released on 2022-01-12. Introduction to Differential Geometry available in PDF, EPUB and Kindle. This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
First Steps in Differential Geometry
First Steps in Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook First Steps in Differential Geometry write by Andrew McInerney. This book was released on 2017. First Steps in Differential Geometry available in PDF, EPUB and Kindle.
