●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
內容簡介
從基因工程到颶風預測，數學模型為我們社會中的許多決策支持指明了方向。如果作為建模基礎的假設和方法是有缺陷的，結果可能極其糟糕。米爾斯切特編著的《數學建模方法與分析(英文版第4版)》對數學建模這一主題給出了嚴謹的論述，提出了一種通用的數學建模方法――五步方法(提出問題、選擇建模方法、推導模型的數學表達式、求解模型、回答問題)，幫助讀者迅速掌握數學建模的真諦。《數學建模方法與分析(英文版第4版)》以引人入勝的方式描述了數學模型的3個主要領域：很優化、動力繫統和隨機過程，引導讀者以實用的方法解決各式各樣的現實問題。
第4版增加了關於粒子跟蹤和異常擴散(包括分數階微積分)的新節。
