Mark M．Meerschaert（米爾斯切特），美國密歇根州立大學概率統(tǒng)計系主任，內(nèi)華達大學物理系教授。他曾在密歇根大學、莫格蘭學院、新西蘭達尼丁Otago大學執(zhí)教，講授過數(shù)學建模、概率、統(tǒng)計學、運籌學、偏微分方程、地下水及地表水水文學與統(tǒng)計物理學課程。他當前的研究方向包括無限方差概率模型的極限定理和參數(shù)估計、金融數(shù)學中的厚尾模型、用厚尾模型及周期協(xié)方差結(jié)構(gòu)建模河水流、異常擴散、連續(xù)時間隨機流動、分數(shù)次導(dǎo)數(shù)和分數(shù)次偏微分方程、地下水流及運輸。
圖書目錄
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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