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內容簡介

This book gives a present-day account of Marston Morse's theory of the calculus of variations in the large. However, there have been Im-portant developments during the past few years which are not mentioned.Let me describe three of these.

內頁插圖

目錄

PREFACE
PART 1 NON-DEGENERATE SMOOTH FUNCTIONS ON A MANIFOLD
Introduction
Definitions and Lenmms
Homotopy Type in TeRns of Critical Values
Examples
The Morse Inequalities
Manifolds in Euclidean Space: The Existence of Non-degenerate Functions
The Lefschetz Theorem on Hyperplane Sections

PART 2 A RAPID COURSE IN RIEMANNIAN GEOMETRY
Covariant Differentiation
The Curvature Tensor
Geodesics and Completeness

PART 3 THE CALCULUS OF VARIATIONS APPLIED TO GEODESICS
The Path Space of a Smooth Manifold
The Fnergy of a Path
The Hessian of the Energy Function at a Critical Path
Jacobi Fields: The Null-space of E**
The Index Theorem
A Finite Dimensional Approximation to nc
The Topology of the Full Path Space
Existence of Non-conjugate Points
Some Between Topology and Curvature

PART 4 APPLICATIONS TO LIE GROUPS AND SYMMEIRIC SPACES
Symmetric Spaces
Lie Groups as Symmetric Spaces
Whole Manifolds of Minimal Geodesics
The Bott Periodicity Theorem for the Unitary Group
The Periodicity Theorem for the Orthogonal Group
APPENDIX THE HOMOTOPY TYPE OF A MONOTONE UNION

前言/序言

莫爾斯理論 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

米爾諾的Morse理論是本專著，雖然不厚，但是將Morse理論講得很透徹，畢竟是大師之作啊

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經典必讀書籍

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不錯……………………………

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milnor 的經典之作。

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書還行吧，就是看不懂，全英文的！！

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J.Milnor ，世界著名數學傢，1962年菲爾茲奬獲得者1989年沃爾夫奬獲得者。Morse理論作為變分學裏麵的重要一部分，已被應用到許多數學分支，我國著名數學傢北京大學張恭慶院士將其推廣至無窮維。

評分☆☆☆☆☆

J.Milnor先生的小品作，買來觀摩

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還是有點偏數學，唉，你說呢

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商品名稱：莫爾斯理論

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