数学建模方法与分析

从基因工程到飓风预测，数学模型为我们社会中的许多决策支持指明了方向。如果作为建模基础的假设和方法是有缺陷的，结果可能极其糟糕。米尔斯切特编著的《数学建模方法与分析(英文版第4版)》对数学建模这一主题给出了严谨的论述，提出了一种通用的数学建模方法――五步方法(提出问题、选择建模方法、推导模型的数学表达式、求解模型、回答问题)，帮助读者迅速掌握数学建模的真谛。《数学建模方法与分析(英文版第4版)》以引人入胜的方式描述了数学模型的3个主要领域：最优化、动力系统和随机过程，引导读者以实用的方法解决各式各样的现实问题。
第4版增加了关于粒子跟踪和异常扩散(包括分数阶微积分)的新节。

Preface
Ⅰ OPTIMIZATION MODELS
1 ONE VARIABLE OPTIMIZATION
1.1 The five-step Method
1.2 Sensitivity Analysis
1.3 Sensitivity and Robustness
1.4 Exercises
2 MULTIVARIABLE OPTIMIZATION
2.1 Unconstrained Optimization
2.2 Lagrange Multipliers
2.3 Sensitivity Analysis and Shadow Prices
2.4 Exercises
3 COMPUTATIONAL METHODS FOR OPTIMIZATION
3.1 One Variable Optimization
3.2 Multivariable Optimization
3.3 Linear Programming
3.4 Discrete Optimization
3.5 Exercises
Ⅱ DYNAMIC MODELS
4 INTRODUCTION TO DYNAMIC MODELS
4.1 Steady State Analysis
4.2 Dynamical Systems
4.3 Discrete Time Dynamical Systems
4.4 Exercises
5 ANALYSIS OF DYNAMIC MODELS
5.1 Eigenvalue Methods
5.2 Eigenvalue Methods for Discrete Systems
5.3 Phase Portraits
5.4 Exercises
6 SIMULATION OF DYNAMIC MODELS
6.1 Introduction to Simulation
6.2 Continuous-Time Models
6.3 The Euler Method
6.4 Chaos and Fractals
6.5 Exercises
Ⅲ PROBABILITY MODELS
7 INTRODUCTION TO PROBABILITY MODELS
7.1 Discrete Probability Models
7.2 Continuous Probability Models
7.3 Introduction to Statistics
7.4 Diffusion
7.5 Exercises
8 STOCHASTIC MODELS
8.1 Markov Chains
8.2 Markov Processes
8.3 Linear Regxession
8.4 Time Series
8.5 Exercises
9 SIMULATION OF PROBABILITY MODELS
9.1 Monte Carlo Simulation
9.2 The Markov Property
9.3 Analytic Simulation
9.4 Particle Tracking
9.5 Fractional Diffusion
9.6 Exercises
Afterword
Index