掃一掃
關注中圖網
官方微博
本類五星書更多>
-
>
宇宙、量子和人類心靈
-
>
氣候文明史
-
>
南極100天
-
>
考研數學專題練1200題
-
>
希格斯:“上帝粒子”的發明與發現
-
>
神農架疊層石:10多億年前遠古海洋微生物建造的大堡礁
-
>
聲音簡史
微分幾何中的初等論題 版權信息
- ISBN：9787510058363
- 條形碼：9787510058363 ; 978-7-5100-5836-3
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
微分幾何中的初等論題 本書特色
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.
微分幾何中的初等論題 內容簡介
本書是一部講述微分幾何的教程。著重講述了n+1維空間中n維旋轉曲面的幾何。通過光滑函數水平集的曲面的講述，這樣不需要更多的預備章節，直接引入全局的概念。向量微積分成為研究該理論的*基本工具。書中講述了測地線，平行輸運、曲率和凸性這些基礎知識，微分形式的介紹僅是為了在積分中的應用。這本教程需要有線性代數、多變量微積分和微分方程的預備知識，供中高級水平的本科生作為一個學期使用。目次：圖論和水平集；向量域；切向空間；曲面；曲面上的向量域；高斯射影；測地線；平行輸運；Weingarten映射；平面曲線的曲率；弧長和線性積分；曲面的曲率；凸曲面；參化曲面；曲面的局部等值和參化曲面；焦點；曲面面積和體積；*小曲面；指數映射；有界曲面；Gauss-Bonnet定理；剛性運動和收斂；等體積的；黎曼矩陣。
微分幾何中的初等論題 目錄
chapter 1
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
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
展開全部
微分幾何中的初等論題 節選
《微分幾何中的初等論題(英文)》適合數學專業本科生、研究生和相關人員閱讀參考。
微分幾何中的初等論題 作者簡介
J. A. Thorpe是國際知名學者，在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用于科研工作者、高校教師和研究生。
書友推薦
- >
姑媽的寶刀
- >
月亮虎
- >
羅曼·羅蘭讀書隨筆-精裝
- >
朝聞道
- >
李白與唐代文化
- >
山海經
- >
大紅狗在馬戲團-大紅狗克里弗-助人
- >
唐代進士錄
本類暢銷
