e-books in Introductory Differential Geometry category
by C.E. Weatherburn - Cambridge University Press , 1955
The book is devoted to differential invariants for a surface and their applications. By the use of vector methods the presentation is both simplified and condensed, and students are encouraged to reason geometrically rather than analytically.
by John Edward Campbell - Clarendon Press , 1926
Contents: Tensor theory; The ground form when n=2; Geodesics in two-way space; Two-way space as a locus in Euclidean space; Deformation of a surface and congruences; Curves in Euclidean space and on a surface; The ruled surface; Minimal surface; etc.
by Theodore Shifrin - University of Georgia , 2015
Contents: Curves (Examples, Arclength Parametrization, Frenet Frame); Surfaces: Local Theory (Parametrized Surfaces, Gauss Map, Covariant Differentiation, Parallel Translation, Geodesics); Surfaces: Further Topics (Holonomy, Hyperbolic Geometry,...).
by Matt Visser - Victoria University of Wellington , 2011
In this text the author presents an overview of differential geometry. Topics covered: Topological Manifolds and differentiable structure; Tangent and cotangent spaces; Fibre bundles; Geodesics and connexions; Riemann curvature; etc.
by Dmitri Zaitsev - Trinity College Dublin , 2004
From the table of contents: Chapter 1. Introduction to Smooth Manifolds; Chapter 2. Basic results from Differential Topology; Chapter 3. Tangent spaces and tensor calculus; Tensors and differential forms; Chapter 4. Riemannian geometry.
by Wulf Rossmann - University of Ottawa , 2003
This is a collection of lecture notes which the author put together while teaching courses on manifolds, tensor analysis, and differential geometry. He offers them to you in the hope that they may help you, and to complement the lectures.
by Balazs Csikos - Eötvös Loránd University , 2010
Contents: Basic Structures on Rn, Length of Curves; Curvatures of a Curve; Plane Curves; 3D Curves; Hypersurfaces; Surfaces in 3-dimensional space; Fundamental equations of hypersurface theory; Topological and Differentiable Manifolds; etc.
by Richard Koch - University of Oregon , 2005
These are differential geometry course notes. From the table of contents: Preface; Curves; Surfaces; Extrinsic Theory; The Covariant Derivative; The Theorema Egregium; The Gauss-Bonnet Theorem; Riemann's Counting Argument.
by Gilbert Weinstein - UAB , 2009
These notes are for a beginning graduate level course in differential geometry. It is assumed that this is the students' first course in the subject. Thus the choice of subjects and presentation has been made to facilitate a concrete picture.
by Peter W. Michor - American Mathematical Society , 2008
Fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.
by Noel J. Hicks - Van Nostrand , 1965
A concise introduction to differential geometry. The ten chapters of Hicks' book contain most of the mathematics that has become the standard background for not only differential geometry, but also much of modern theoretical physics and cosmology.
by Gabriel Lugo - University of North Carolina at Wilmington , 2006
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.
by Ruslan Sharipov - Samizdat Press , 2004
Textbook for the first course of differential geometry. It covers the theory of curves in three-dimensional Euclidean space, the vectorial analysis both in Cartesian and curvilinear coordinates, and the theory of surfaces in the space E.
by Stefan Waner , 2005
Smooth manifolds and scalar fields, tangent vectors, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, the Riemann curvature tensor, premises of general relativity.
by Nigel Hitchin , 2003
The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.
by Edward Nelson - Princeton Univ Pr , 1974
The lecture notes for the first part of a one-term course on differential geometry given at Princeton in the spring of 1967. They are an expository account of the formal algebraic aspects of tensor analysis using both modern and classical notations.