mark
m．meerschaert，美国密歇根州立大学概率统计系教授。他曾在密歇根大学、英格兰学院、内华达大学、新西兰达尼丁otago大学执教，讲授过数学建模、概率、统计学、运筹学、偏微分方程、地下水及地表水水文学与统计物理学课程。他当前的研究方向包括无限方差概率模型的极限定理和参数估计、金融数学中的厚尾模型、用厚尾模型及周期协方差结构建模河水流、医学成像、异常扩散、连续时间随机游动、分数次导数和分数次偏微分方程、地下水流及运输。
目錄：
《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
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