微分幾何

前言

　　The ISFMA-CIMPA School on "Differential Geometry: Theory andApplications" was held on 07 August - 18 August 2006， in the building ofthe Chinese-French Institute for Applied Mathematics （ISFMA）, FudanUniversity, Shanghai, China. This school was jointly organized by theISFMA and the CIMPA （International Centre for Pure and AppliedMathematics）, Nice, France. About sixty participants from China, HongKong, France, Cambodia, India, Iran, Pakistan, Philippines, Romania,Russia, Sri-Lanka, Thailand, Turkey, Uzbekistan and Vietnam attendedthis highly successful event.　　The first objective of this school was to lay down in a self-contained:and accessible manner the basic notions of differential geometry, suchasthe metric tensor, the Riemann curvature tensor, the fundamental formsof a surface, covariant derivatives, and the fundamental theorem of sur-face theory etc. Although this field is with good reasons often consideredas a "classical" one, it has been recently "rejuvenated", thanks to themanifold applications where it plays an essential role.　　The second objective of this school was to present some of theseapplications, such as the theory of linearly and nonlinearly elastic shells,the implementation of numerical methods for shells, and mesh generationin finite element methods.　　To fulfill these objectives, four series of lectures, each series compris-ing ten 50min-lectures, were delivered under the following titles: "In-troduction to differential geometry", "Introduction to shell theory", "Adifferential geometry approach to mesh generation", and "Numericalmethods for shells". This volume gathers the materials covered in theselectures. As such, this volume should be very useful to graduate studentsand researchers in pure and applied mathematics.　　The organizers take pleasure in thanking the various organizations fortheir generous support: The ISFMA, the CIMPA, the French Embassyin Beijing, the Consulate General of France in Shanghai, the NationalNatural Science Foundation of China, Fudan University, Higher Educa-tion Press and World Scientific. Finally, our special thanks are due toMrs. Zhou Chun-Lian for her patient and effective work in editing thisbook.

內(nèi)容概要

This book gives the basic notions of differential geometry,such as the metric tensor, the Riemann curvature tensor,the fundamental forms of a surface, covariant derivatives,and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a "classical" one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells,such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods. This volume will be very useful to graduate students and researchers in pure and applied mathematics.

作者簡介

　　李大潛，數(shù)學家。江蘇南通人。1957年畢業(yè)于復旦大學數(shù)學系，1966年該校在職研究生畢業(yè)。1997年當選為第三世界科學院院士。復旦大學教授。中國工業(yè)與應用數(shù)學學會理事長，中國數(shù)學會副理事長，中法應用數(shù)學研究所所長。對一般形式的二自變數(shù)擬線性雙曲型方程組的自由邊界問題和間斷解的系統(tǒng)研究，以及對非線性波動方程經(jīng)典解的整體存在性及生命跨度的完整結(jié)果，均處于國際領(lǐng)先地位，得到國際上的高度評價。在理論研究的基礎上，對各種電阻率測井建立了統(tǒng)一的數(shù)學模型和方法，并成功地在國內(nèi)10多個油田推廣使用。1995年當選為中國科學院院士。

書籍目錄

PrefacePhilippe G. Ciarlet: An Introduction to Differential Geometry in R 3Philippe G. Ciarlet, Cristinel Mardare: An Introduction to Shell TheoryDominique Chapelle: Some New Results and Current Challenges in the Finite Element Analysis of ShellsPascal Frey: A Differential Geometry Approach to Mesh Generation

圖書封面

圖書標簽Tags

無

評論、評分、閱讀與下載

---

    微分幾何 PDF格式下載

---