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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.

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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 格式

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春色滿園關不住，一枝紅杏齣牆來

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不錯

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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.

評分☆☆☆☆☆

1960年代的書，字體太難看瞭……看著纍人，印刷也太差瞭。還不如買中文版的……

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不錯……………………………

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莫爾斯理論的經典教材，是本研究領域不可不讀的教材

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米爾諾的經典名著，數學寫作的典範！

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經典書籍，必讀

評分☆☆☆☆☆

1960年代的書，字體太難看瞭……看著纍人，印刷也太差瞭。還不如買中文版的……

類似圖書 點擊查看全場最低價