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实用数学：建模、分析、逼近（影印版）

作者：
Sam Howison
定价：
40.00元
ISBN：
978-7-04-023607-1
版面字数：
380.000千字
开本：
16开
全书页数：
326页
装帧形式：
平装
重点项目：
暂无
出版时间：
2008-03-28
读者对象：
高等教育
一级分类：
数学与统计学类
二级分类：
数学与应用数学专业课
三级分类：
其他课程
暂无
  • Preface
  • PartI Modelling techniques
    • 1 The basics of modelling
      • 1.1 Introduction
      • 1.2 What do we mean by a model?
      • 1.3 Principles of modelling: physical laws and constitutive relations
      • 1.4 Conservation laws
      • 1.5 General remarks
      • 1.6 Exercises
    • 2 Units, dimensions and dimensional analysis
      • 2.1 Introduction
      • 2.2 Units and dimensions
      • 2.3 Electric fields and electrostatics
      • 2.4 Sources and further reading
      • 2.5 Exercises
    • 3 Nondimensionalisation
      • 3.1 Nondimensionalisation and dimensionless parameters
      • 3.2 The Navier-Stokes equations and Reynolds numbers
      • 3.3 Buckingham's Pi-theorem
      • 3.4 Sources and further reading
      • 3.5 Exercises
    • 4 Case studies: hair modelling and cable laying
      • 4.1 The Euler-Bernoulli model for a beam
      • 4.2 Hair modelling
      • 4.3 Undersea cable laying
      • 4.4 Modelling and analysis
      • 4.5 Sources and further reading
      • 4.6 Exercises
    • 5 Case study: the thermistor （1）
      • 5.1 Heat and current flow in thermistors
      • 5.2 Nondimensionalisation
      • 5.3 A thermistor in a circuit
      • 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
      • 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
      • 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

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