●Introduction
●Preface
●Chapter 1 Variational Method
●1.1.Functional and Its Extremal Problems
●1.1.1.The conception of functional
●1.1.2.The extremes of functionals
●1.2.The Variational of Functionals and the Simplest Euler Equation
●1.2.1.The variational of functionals
●1.2.2.The simplest Euler equation
●1.3.The Cases of Multifunctions and Multivariates
●1.3.1.Multifunctions
●1.3.2.Multivariates
●1.4.Functional Extremes under Certain Conditions
●1.4.1.Isoperimetric problem
●1.4.2.Geodesic problem
●1.5.Natural Boundary Conditions
●1.6.Variational Principle
●1.6.1.Variational principle of classical mechanics
●1.6.2.Variational principle of quantummechanics
●1.7.The Applications of the Variational Method in Physics......
內容簡介
本書是為從事物理學與其他理工科研究人員和非數學類研究生與本科高年級學生撰寫的數學方面的基礎理論讀物和參考書。對於物理和其他理工學科做研究工作時所必須要用到的數學知識做了比較詳細和全面的介紹,包括變分法,希爾伯特空間,二階常微分方程,貝塞爾函數,狄拉函數,格林函數,範數與測度,積分方程,數論在物理逆問題中的應用,高維空間中的基本方程等內容。本書的寫作力求概念說明清楚,公式推導詳盡,內容深入淺出。便於讀者學習。