莫爾斯理論 epub pdf mobi txt 電子書 下載 2024

莫爾斯理論 epub pdf mobi txt 電子書 下載 2024

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莫爾斯理論 epub pdf mobi txt 電子書 下載 2024

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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 epub pdf mobi txt 電子書 下載 2024

莫爾斯理論 下載 epub mobi pdf txt 電子書

評分☆☆☆☆☆

米爾諾的經典名著，數學寫作的典範！

評分☆☆☆☆☆

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.

評分☆☆☆☆☆

幫人買的，很好很經典的專業書。

評分☆☆☆☆☆

非常好，不錯不錯。。。

評分☆☆☆☆☆

　　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.

評分☆☆☆☆☆

數學名著，非常經典，推薦

評分☆☆☆☆☆

如果有興趣瞭解莫爾斯理論的，可以參考

評分☆☆☆☆☆

Milnor 的經典之作！

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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