作者：索普
页数：253
出版社：世界图书出版公司
出版日期：2013
ISBN：9787510058363
电子书格式：pdf/epub/txt
内容简介
本书是一部讲述微分几何的教程。着重讲述了n+1维空间中n维旋转曲面的几何。通过光滑函数水平集的曲面的讲述，这样不需要更多的预备章节，直接引入全局的概念。向量微积分成为研究该理论的最基本工具。书中讲述了测地线，平行输运、曲率和凸性这些基础知识，微分形式的介绍仅是为了在积分中的应用。这本教程需要有线性代数、多变量微积分和微分方程的预备知识，供中高级水平的本科生作为一个学期使用。目次：图论和水平集；向量域；切向空间；曲面；曲面上的向量域；高斯射影；测地线；平行输运；Weingarten映射；平面曲线的曲率；弧长和线性积分；曲面的曲率；凸曲面；参化曲面；曲面的局部等值和参化曲面；焦点；曲面面积和体积；最小曲面；指数映射；有界曲面；Gauss-Bonnet定理；刚性运动和收敛；等体积的；黎曼矩阵。
作者简介
J. A. Thorpe是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
in the past decade there has been a significant change in the freshman/sophomore mathematics curriculum as taught at many， if not most， of our colleges. this has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. the advanta8;es of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. several textbooks adopting this point of view are now available and have been widely adopted. students completing the sophomore year now have a fair preliminary understanding of spaces of many dimensions.
目录
graphs and level sets
chapter 2
vector fields
chapter 3
the tangent space
chapter 4
surfaces
chapter 5
vector fields on surfaces; orientation
chapter 6
the gauss map
chapter 7
geodesics
chapter 8
parallel transport
chapter 9
the weingarten map
chapter 10
curvature of plane curves
chapter 11
arc length and line integrals
chapter 12
curvature of surfaces
chapter 13
convex surfaces
chapter 14
parametrized surfaces
chapter 15
local equivalence of surfaces and parametrized surfaces
chapter 16
focal points
chapter 17
surface area and volume
chapter 18
minimal surfaces
chapter 19
the exponential map
chapter 20
surfaces with boundary
chapter 21
the gauss-bonnet theorem
chapter 22
rigid motions and congruence
chapter 23
isometries
chapter 24
riemannian metrics
bibliography
notational index
subject index
节选
《微分几何中的初等论题(英文)》适合数学专业本科生、研究生和相关人员阅读参考。
