非线性泛函分析及其应用·第4卷：在数学物理中的应用

　　第4卷主要论述非线性泛函分析在数学物理中（包括力学、弹性学、塑性学、流体运动学、热力学、统计力学、狭义相对论和广义相对论、宇宙学等）的应用。给出有关的物理背景及有关的基本方程，用泛函分析的经典和现代结果对在物理学发展中起重要作用的重要问题进行深入讨论。是一本沟通物理学和数学的好书。

暂缺《非线性泛函分析及其应用·第4卷：在数学物理中的应用》作者简介

Ⅰ Introduction
　1 Foreign exchange markets
　　1.1 Introduction
　　1.2 Historical background
　　1.3 Forex as an asset class
　　1.4 Spot forex
　　1.5 Derivatives: forwards, futures, calls, puts, and all that
　　1.6 References and further reading
Ⅱ Mathematical preliminaries
　2 Elements of probability theory
　　2.1 Introduction
　　2.2 Probabihty spaces
　　2.4 Convergence of random variables and limit theorems
　　2.5 References and further reading
　3 Discrete-time stochastic engines
　　3.1 Introduction
　　3.3 Binomial stochastic engines for single- and multi-period markets
　　3.4 Multinomial stochastic engines
　　3.5 References and further reading
4 　Continuous-time stochastic engines
　　4.1 Introduction
　　4.2 Stochastic processes
　　4.3 Markov processes
　　4.5 Wiener processes
　　4.6 Poisson processes
　　4.7 SDE and Mappings
　　4.9 SDEs for jump-diffusions
　　4.10 Analytical solution of PDEs
　　　4.10.1 Introduction
　　　4.10.2 The reduction method
　　　4.10.3 The Laplace transform method
　　　4.10.4 The eigenfunction expansion method
　　4.11 Numerical solution of PDEs
　　　4.11.2 Explicit, implicit, and Crank-Nicalson schemes for solving one-dimensional problems
　　　4.11.3 ADI scheme for solving two-dimensional problems
　　4.12 Numerical solution of SDEs
　　　4.12.1 Introduction
　　　4.12.2 Formulation of the problem
　　　4.12.3 The Maruler-Maruyama scheme
　　　4.13 References and further reading
Ⅲ Discrete-time models
　5 Single-period markets
　　5.1 Introduction
　　5.2 Binomial markets with nonrisky investments
　　5.3 Binomial markets without nonrisky investments
　　5.4 General single-period markets
　　5.6 Pricing of contingent claims
　　5.7 Elementary portfolio theory
　……
Ⅳ Continuous-time models
Bibliography
Index