數學建模方法與分析（英文版·第4版） pdf epub mobi txt 電子書 下載2025

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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瞭方嚮。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。《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齣瞭嚴謹的論述，提齣瞭一種通用的數學建模方法五步方法（提齣問題、選擇建模方法、推導模型的數學錶達式、求解模型、迴答問題），幫助讀者迅速掌握數學建模的真諦。作者以引人入勝的方式描述瞭數學模型的3個主要領域：最優化、動力係統和隨機過程，引導讀者以實用的方法解決各式各樣的現實問題。

第4版增加瞭關子粒子跟蹤和異常擴散（包括分數階微積分）的新節。

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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