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内容简介
数学建模这门课程在数学及其在各个领域的应用之间架起一座桥梁。本书介绍了速个建模过程的原理，通过本书的学习，学生将有机会在以下建模活动中亲身实践，增强解决问题的能力；设计创意模型和经验模型、模型分析以及模型研究。 本书特点 论证了离散动态系统、离散优化和仿真等技术如何促进现代应用数学的发展 强调通过模型设计提高学生的创造性，展现模型构建的艺术特性，包括经验建模和仿真建模的思想 将数学建模方法与多样化建模和置信度建立等更具创造性的方面结合起来 在设计创意模型和经验模型、模型分析以及模型研究中融入个人项目和小组项目，并且包含大量的例子和习题随书光盘包含软件、附加的建模场景和项目以及过去数学建模竞赛的题目
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顾客评论
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目录
目 录 1 Modeling Change 1 Introduction 1 Example 1: Testing for Proportionality 2 1.1 Modeling Change with Difference Equations 4 Example I: A Savings Certificate 5 Example 2: Mortgaging a Home 6 1.2 Approximating Change with Difference Equations Example 1: Growth of a Yeast Culture 9 Example 2: Growth of a Yeast Culture Revisited 10 Example 3: Spread of a Contagious Disease 12 Example 4: Decay of Digoxin in the Bloodstream 13 Example 5: Heating of a Cooled Object 14 1.3 Solutions to Dynamical Systems 18 Example 1: A Savings Certificate Revisited 18 Example 2: Sewage Treatment 21 Example 3: PreScription for Digoxin 25 Example 4: An Investment Annuity 26 Example 5: A Checking Account 28 Example 6: An Investment Annuity Revisited 30 1.4 Systems of Difference Equations 35 Example I: A Car Rental Company 35 Example 2: The Battle of Trafalgar 38 Example 3: Competitive Hunter Model--Spotted Owls and Hawks Example 4: Voting Tendencies of the Political Parties 44 2 The Modeling Process, Proportionality, and Geometric Similarity Introduction 52 2.1 Mathematical Models 54 Example 1: Vehicular Stopping Distance 59 2.2 Modeling Using Proportionality 65 Example 1: Kepler''''s Third Law 67 2.3 Modeling Using Geometric Similarity 75 Example 1: Raindrops from a Motionless Cloud 77 Example 2: Modeling a Bass Fishing Derby 79 2.4 Automobile Gasoline Mileage 88 2.5 Body Weight and Height, Strength and Agility 91 Model Fitting 97 Introduction 97 3.1 Fitting Models to Data Graphically 101 3.2 Analytic Methods of Model Fitting 107 3.3 Applying the Least-Squares Criterion 114 3.4 Choosing a Best Model 119 Example 1: Vehicular Stopping Distance 122 4 Experimental Modeling 126 Introduction 126 4.1 Harvesting in the Chesapeake Bay and Other One-Term Models 127 Example 1: Harvesting Bluefish 130 Example 2: Harvesting Blue Crabs 131 4.2 High-Order Polynomial Models 138 Example 1: Elapsed Time of a Tape Recorder 140 4.3 Smoothing: Low-Order Polynomial Models 146 Example 1: Elapsed Time of a Tape Recorder Revisited 147 Example 2: Elapsed Time of a Tape Recorder Revisited Again Example 3: Vehicle Stopping Distance 153 Example 4: Growth of a Yeast Culture 155 4.4 Cubic Spline Models 159 Example 1: Vehicle Stopping Distance Revisited 167 5 Simulation Modeling 175 Introduction 175 5.1 Simulating Deterministic Behavior:Area Under a Curve 5.2 Generating Random Numbers 182 5.3 Simulating Probabilistic Behavior ''''186 5.4 Inventory Model: Gasoline and Consumer Demand 194 5.5 Queuing Models 205 Example 1: A Harbor System 205 Example 2: Morning Rush Hour 213 6 Discrete Probabilistic Modeling 217 Introduction 217 6.1 Probabilistic Modeling with Discrete Systems 217 Example 1: Rental Car Company Revisited 217 Example 2: Voting Tendencies 219 6.2 Modeling Component and System Reliability 223 Example 1: Series Systems 224 Example 2: Parallel Systems 224 Example 3: Series and Parallel Combinations 224 6.3 Linear Regression 227 Example 1: Ponderosa Pines 229 Example 2: The Bass Fishing Derby Revisited 231 7 Discrete Optimization Modeling 236 7.1 An Overview of Discrete Optimization Modeling 237 Example 1: Determining a Production Schedule 237 Example 2: Space Shuttle Cargo 240 Example 3: Approximation by a Piecewise Linear Function 241 7.2 Linear Programming h Geometric Solutions 250 Example 1: The Carpenter''''s Problem 251 Example 2: A Data-Fitting Problem 252 7.3 Linear Programming Ih Algebraic Solutions 259 Example 1: Solving the Carpenter''''s Problem Algebraically 261 7.4 Linear Programming III: The Simplex Method 263 Example 1: The Carpenter''''s Problem Revisited 268 Example 2: Using the Tableau Format 271 7.5 Linear Programming IV: Sensitivity Analysis 273 7.6 Numerical Search Methods 279 Example 1: Using the Dichotomous Search Method 282 Example 2: Using the Golden Section Search Method 285 Example 3: Model-Fitting Criterion Revisited 287 Example 4: Optimizing Industrial Flow 288 8 Dimensional Analysis and Similitude 292 Introduction 292 8.1 Dimensions as Products 295 Example 1: A Simple Pendulum 298 Example 2: Wind Force on a Van 301 8.2 The Process of Dimensional Analysis 304 Example l: Terminal Velocity of a Raindrop 309 Example 2: Automobile Gas Mileage Revisited 311 8.3 A Damped Pendulum 313 8.4 Examples Illustrating Dimensional Analysis 319 Example I : Explosion Analysis 319 Example 2: How Long Should You Roast a Turkey 324 8.5 Similitude 330 Example I: Drag Force on a Submarine 331 9 Graphs of Functions as Models 336 9.1 An Arms Race 336 Example 1: Civil Defense 345 Example 2: Mobile Launching Pads 346 Example 3: Multiple Warheads 347 Example 4: MIRVs Revisited: Counting Warheads 348 9.2 Modeling an Arms Race in Stages 350 9.3 Managing Nonrenewable Resources: The Energy Crisis 9.4 Effects of Taxation on the Energy Crisis 359 9.5 A Gasoline Shortage and Taxation 364 10 Modeling with a Differential Equation 368 Introduction 368 10.1 Population Growth 371 10.2 Prescribing Drug Dosage 10.3 Braking Distance Revisited 391 10.4 Graphical Solutions of Autonomous Differential Equations Example 1: Drawing a Phase Line and Sketching Solution Curves 396 Example 2: Cooling Soup 399 Example 3: Logistic Growth Revisited 400 10.5 Numerical Approximation Methods 404 Example 1: Using Euler''''s Method 406 Example 2: A Savings Certificate Revisited 407 11 Modeling with Systems of Differential Equations 412 Introduction 412 11.1 Graphical Solutions of Autonomous Systems of First-Order Differential Equations 413 Example 1: A Linear Autonomous System 414 Example 2: A Nonlinear Autonomous System 415 11.2 A Competitive Hunter Model 419 11.3 A Predator-Prey Model 427 11.4 Two Military Examples 437 Example I: Lanchester Combat Models 437 Example 2: Economic Aspects of an Arms Race 444 11.5 Euler''''s Method for Systems of Differential Equations 450 Example 1: Using Euler'''' s Method for Systems 451 Example 2: A Trajectory and Solution Curves 452 12 Continuous Optimization Modeling 458 Introduction 458 12.1 An Inventory Problem: Minimizing the Cost of Delivery and Storage 459 12.2 A Manufacturing Problem: Maximizing Profit in Producing Competing Products 468 12.3 Constrained Continuous Optimization 474 Example l: An Oil Transfer Company 474 Example 2: A Space Shuttle Water Container 476 12.4 Managing Renewable Resources: The Fishing Industry 480 A Problems from the Mathematics Contest in Modeling. 1985-2002 490 B An Elevator Simulation Algorithm s23 C The Revised Simplex Method Index 535
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