实用数学:建模分析逼近

《实用数学:建模分析逼近》是由高等教育出版社出版编著的实体书。《实用数学:建模分析逼近(影印版)来自》内容分为三部分:建模，讲述了建模的一些原则(包括物理定律、本构关系及守恒定律)，住良坏听说听量纲分析(包括Buckingham的Pi定理)等;分析技巧360百科，讲述了偏微分方程和广义函数的基础知识;渐近息般保层须黑并混分析，讲述了渐近展开的基本概念，正则摄动展开，边界层和多重尺度法等。

• 书名 实用数学:建模分析逼近
• 别名 Practical Applied Mathematics: Modeling, Analysis, Approximation
• ISBN 9787040236071
• 页数 326页
• 出版社 高等教育出版社

　误敌起动感气否细　目录

　　Preface

　　Part Ⅰ Modelling techniques

　　1 The basics of modelli么待动书配什持基钱ng

　　1.1 Introduction

　　1.2 What do we mean by a model?

　　1.3 Principles of modelling: physical laws and constitutive relations

　　1.4 Conserv来自ation laws

　　1.5 General remarks

　　1.6 Exercises

　　2 Units, dimensions and 360百科dimensional analysis

　　2.1 Introduction

　　2.2 Units and dimensions

　　2.3 Electric fields and electrostatics

　　2.4 Sources and further reading

　　2.5 Exer右立cises

　　3 被周顾大Nondimensionalisation

　　3.1 Nondimensi吧养委具onalisation and dimensionless parameters

　　3.2 The Navier-Stoke战集流s equations and R扬调常eynolds numbers

　　3.3 Buckingham's Pi-theorem

　　3.4 Sour妈材ces and further reading

　　3.5 Exercises

　　4 Case studies: hair modelling and cable laying

　　4.1 The Euler吗探袁编-Bernoulli model for a 此温beam

　　4.2 Hair m慢非企井扬庆散断odelling

势候　　4.3 Undersea cable laying

　　4.4 Modelling and analysis

　　4.5 Sources and further reading

　　4.6 Exercise

　　5 C钢危燃期京事抓示意款接ase study: the thermistor (1)

　　5.1 Heat and current flow in th即ermistors

　　头记更5.2 Nondimens讲ionalisation

　　5.3 A thermi呢烟视线办原stor in a cir供觉轴工如乙深cuit

　　5.4 Sources and further reading

　　5.5 Exercises

　　6 Case study: electrostatic painting

　　6.1 Electrostatic painting

　　6.2 Field equations

　　6.3 Boundary conditions

　　6.4 Nondimensionalisation

　　6.5 Sources and further reading

　　6.6 Exercises

　　Part Ⅱ Analytical techniques

　　7 Partial differential equations

　　7.1 First-order quasilinear partial differential equations: theory

　　7.2 Example: Poisson processes

　　7.3 Shocks

　　7.4 Fully nonlinear equations: Charpit's method

　　7.5 Second-order linear equations in two variables

　　7.6 Further reading

　　7.7 Exercises

　　8 Case study: traffic modelling

　　8.1 Simple models for traffic flow

　　8.2 Traffic jams and other discontinuous solutions

　　8.3 More sophisticated models

　　8.4 Sources and further reading

　　8.5 Exercises

　　9 The delta function and other distributions

　　9.1 Introduction

　　9.2 A point force on a stretched string; impulses

　　9.3 Informal definition of the delta and Heaviside functions

　　9.4 Examples

　　9.5 Balancing singularities

　　9.6 Green's functions

　　9.7 Sources and further reading

　　9.8 Exercises

　　10 Theory of distributions

　　10.1 Test functions

　　10.2 The action of a test function

　　10.3 Definition of a distribution

　　10.4 Further properties of distributions

　　10.5 The derivative of a distribution

　　10.6 Extensions of the theory of distributions

　　10.7 Sources and further reading

　　10.8 Exercises

　　11 Case study: the pantograph

　　11.1 What is a pantograph?

　　11.2 The model

　　11.3 Impulsive attachment for an undamped pantograph

　　11.4 Solution near a support

　　11.5 Solution for a whole span

　　11.6 Sources and further reading

　　11.7 Exercises

　　Part Ⅲ Asymptotic techniques

　　12 Asymptotic expansions

　　12.1 Introduction

　　12.2 Order notation

　　12.3 Convergence and divergence

　　12.4 Further reading

　　12.5 Exercises

　　13 Regular perturbation expansions

　　13.1 Introduction

　　13.2 Example: stability of a spacecraft in orbit

　　13.3 Linear stability

　　13.4 Example: the pendulum

　　13.5 Small perturbations of a boundary

　　13.6 Caveat expandator

　　13.7 Exercises

　　14 Case study: electrostatic painting (2)

　　14.1 Small parameters in the electropaint model

　　14.2 Exercises

　　15 Case study: piano tuning

　　15.1 The notes of a piano: the tonal system of Western music

　　15.2 Tuning an ideal piano

　　15.3 A real piano

　　15.4 Sources and further reading

　　15.5 Exercises

　　16 Boundary layers

　　16.1 Introduction

　　16.2 Functions with boundary layers; matching

　　16.3 Examples from ordinary differential equations

　　16.4 Case study: cable laying

　　16.5 Examples for partial differential equations

　　16.6 Exercises

　　17 Case study: the thermistor (2)

　　17.1 Strongly temperature-dependent conductivity

　　17.2 Exercises

　　18 Lubrication theory' analysis in long thin domains

　　18.1 Lubrication theory' approximations: slender geometries

　　18.2 Heat flow in a bar of variable cross-section

　　18.3 Heat flow in a long thin domain with cooling

　　18.4 Advection-diffusion in a long thin domain

　　18.5 Exercises

　　19 Case study: continuous casting of steel

　　19.1 Continuous casting of steel

　　19.2 Exercises

　　20 Lubrication theory for fluids

　　20.1 Thin fluid layers: classical lubrication theory

　　20.2 Thin viscous fluid sheets on solid substrates

　　20.3 Thin fluid sheets and fibres

　　20.4 Further reading

　　20.5 Exercises

　　21 Case study: turning of eggs during incubation

　　21.1 Incubating eggs

　　21.2 Modelling

　　21.3 Exercises

　　22 Multiple scales and other methods for nonlinear oscillators

　　22.1 The Poincare-Linstedt method

　　22.2 The method of multiple scales

　　22.3 Relaxation oscillations

　　22.4 Exercises

　　23 Ray theory and the WKB method

　　23.1 Introduction

　　23.2 Classical WKB theory

　　23.3 Geometric optics and ray theory: why do we say light travels in straight lines?

　　23.4 Kelvin's ship waves

　　23.5 Exercises

　　References

　　Index