| “这是一本很好的数学建模教科书，其中的数学知识非常有用，符合本科生数学建模课程的教学要求。” ——Tohn E.Doner，加州大学圣芭芭拉分校数学系 |
| Mark M.Meerschaert美国密歇根州立大学概率统计系主任，内华达大学物理系教授。他曾在密歇根大学，英格兰学院、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、异常扩散、连续时间随机流动、分数次导数和分数次偏微分方程、地下水流及运输。 |
| 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 Fractais 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 Regression 8.4 Time Series 8.5 Exercises 9 SIMULATION OF PROBABILITY MODELS 9.1 Monte Carlo Simulation 9.2 The MarkovProperty 9.3 Analytic Simulation 9.4 Exercises Afterword Index |
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