莫尔斯理论 下载 mobi epub pdf 电子书 2025

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内容简介

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.

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目录

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

莫尔斯理论 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

米尔诺的Morse理论是本专著，虽然不厚，但是将Morse理论讲得很透彻，毕竟是大师之作啊

评分☆☆☆☆☆

非常棒，经典著作，值得购买！

评分☆☆☆☆☆

J.Milnor ，世界著名数学家，1962年菲尔兹奖获得者1989年沃尔夫奖获得者。Morse理论作为变分学里面的重要一部分，已被应用到许多数学分支，我国著名数学家北京大学张恭庆院士将其推广至无穷维。

评分☆☆☆☆☆

不错，活动时买的，挺划算的。

评分☆☆☆☆☆

1960年代的书，字体太难看了……看着累人，印刷也太差了。还不如买中文版的……

评分☆☆☆☆☆

教材不能随便选，这本莫尔斯理论才对

评分☆☆☆☆☆

大家的东西就是好读

评分☆☆☆☆☆

J.Milnor ，世界著名数学家，1962年菲尔兹奖获得者1989年沃尔夫奖获得者。Morse理论作为变分学里面的重要一部分，已被应用到许多数学分支，我国著名数学家北京大学张恭庆院士将其推广至无穷维。

评分☆☆☆☆☆

Milnor 的经典之作！

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