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。《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。作者以引人入胜的方式描述了数学模型的3个主要领域:*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版增加了关子粒子跟踪和异常扩散(包括分数阶微积分)的新节。
数学建模方法与分析-英文版-第4版_(美)米尔斯切特_机械工业出版社_

《数学建模方法与分析(英文版)(第4版)》
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 probabiuty 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 regression
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