莫尔斯理论 epub pdf mobi txt 电子书 下载 2025

莫尔斯理论 epub pdf mobi txt 电子书 下载 2025

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莫尔斯理论 epub pdf mobi txt 电子书 下载 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.

内页插图

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 epub pdf mobi txt 电子书 下载 2025

莫尔斯理论 下载 epub mobi pdf txt 电子书 2025

评分☆☆☆☆☆

真的很薄的的一本书。

评分☆☆☆☆☆

书很薄，读起来很深刻，好书！

评分☆☆☆☆☆

　　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.

评分☆☆☆☆☆

很好的一本数学书，推荐

评分☆☆☆☆☆

　　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.

评分☆☆☆☆☆

milnor 的经典之作。

评分☆☆☆☆☆

　　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.

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

不错……………………………

类似图书 点击查看全场最低价