數(shù)學(xué)建模方法與分析

前言

Mathematical modeling is the link between mathematics and the rest of the world. You ask a question. You think a bit, and then you refine the question, phrasing it in precise mathematical terms. Once the question becomes a mathematics question, you use mathematics to find an answer. Then finally (and this is the part that too many people forget), you have to reverse the process, translating the mathematical solution back into a comprehensible, no-nonsense answer to the original question. Some people are fluent in English, and some people are fluent in calculus. We have plenty of each. We need more people who are fluent in both languages and are willing and able to translate. These are the people who will be influential in solving the problems of the future.This text, which is intended to serve as a general introduction to the area of mathematical modeling, is aimed at advanced undergraduate or beginning graduate students in mathematics and closely related fields. Formal prerequisites consist of the usual freshman-sophomore sequence in mathematics, including one-variable calculus, multivariable calculus, linear algebra, and differential equations. Prior exposure to computing and probability and statistics is useful, but is not required.

內(nèi)容概要

本書提出了一種通用的數(shù)學(xué)建模方法——五步方法。幫助讀者迅速掌握數(shù)學(xué)建模的真諦。作者以引人入勝的方式描述了數(shù)學(xué)模型的3個主要領(lǐng)域：最優(yōu)化、動力系統(tǒng)和隨機過程。本書以實用的方法解決各式各樣的現(xiàn)實問題，包括空間飛船的對接、傳染病的增長率和野生生物的管理等。此外，本書根據(jù)需要詳細介紹了解決問題所需要的數(shù)學(xué)知識?！　”景嫘略鰞?nèi)容：　　增加了關(guān)于時間序列分析和擴散模型的新節(jié)?！　￡P(guān)注國際性問題，如經(jīng)濟預(yù)測、人口控制、蓄水池。此外，更新了最優(yōu)化問題。

作者簡介

Mark M.Meerschaert美國密歇根州立大學(xué)概率統(tǒng)計系主任，內(nèi)華達大學(xué)物理系教授。他曾在密歇根大學(xué)，英格蘭學(xué)院、新西蘭達尼丁Otago大學(xué)執(zhí)教，講授過數(shù)學(xué)建模、概率、統(tǒng)計學(xué)、運籌學(xué)、偏微分方程、地下水及地表水水文學(xué)與統(tǒng)計物理學(xué)課程。他當(dāng)前的研究方向包括無限方差概率

書籍目錄

PrefaceⅠ 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  ExercisesⅡ   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  ExercisesⅢ   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  ExercisesAfterwordIndex

章節(jié)摘錄

Problems in optimization are the most common applications of mathematics. Whatever the activity in which we are engaged, we want to maximize the good that we do and minimize the unfortunate consequences or costs. Business managers attempt to control variables in order to maximize profit or to achieve a desired goal for production and delivery at a minimum cost. Managers of renewable resources such as fisheries and forests try to control harvest rates in order to maximize long-term yield. Government agencies set standards to minimize the environmental costs of producing consumer goods. Computer system managers try to maximize throughput and minimize delays. Farmers space their plantings to maximize yield. Physicians regulate medications to minimize harmful side effects. What all of these applications and many more have in common is a particular mathematical structure. One or more variables can be controlled to produce the best outcome in some other variable, subject in most cases to a variety of practical constraints on the control variables. Optimization models are designed to determine the values of the control variables which lead to the optimal outcome, given the constraints of the problem.We begin our discussion of optimization models at a place where most students will already have some practical experience. One-variable optimization problems, sometimes called maximum-minimum problems, are typically discussed in first semester calculus. A wide variety of practical applications can be handled using just these techniques. The purpose of this chapter, aside from a review of these basic techniques, is to introduce the fundamentals of mathematical modeling in a familiar setting.

媒體關(guān)注與評論

“這是一本很好的教學(xué)建模教科書，其中的數(shù)學(xué)知識非常有用，符合本科生數(shù)學(xué)建模課程的教學(xué)要求。”  ——Iohn E Doner.加州大學(xué)圣芭芭拉分校數(shù)學(xué)系  

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《數(shù)學(xué)建模方法與分析(英文版·第3版)》為經(jīng)典原版書庫叢書之一，由機械工業(yè)出版社出版。

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