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【数学建模】A First Course in Mathematical Modeling-[5]-[pdf]-[Frank R. Giordano, William P. Fox, Steven B. Horton]

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    发表于 2017-10-13 15:06:35 | 显示全部楼层 |阅读模式
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    书籍信息:
    标题: A First Course in Mathematical Modeling【数学建模】
    语言: English
    格式: pdf
    大小: 11.8M
    页数: 796
    年份: 2013
    作者: Frank R. Giordano, William P. Fox, Steven B. Horton
    版次: 5
    出版社: Cengage Learning


    简介

    Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.


    目录
    Cover
    ......Page 1
    Title Page
    ......Page 3
    Copyright
    ......Page 4
    Contents......Page 5
    Additional Contents on Website......Page 14
    Preface......Page 17
    Introduction......Page 25
    1.1: Modeling Change with Difference Equations......Page 28
    1.2: Approximating Change with Difference Equations......Page 34
    1.3: Solutions to Dynamical Systems......Page 42
    1.4: Systems of Difference Equations......Page 61
    Introduction......Page 82
    2.1: Mathematical Models......Page 84
    2.2: Modeling Using Proportionality......Page 94
    2.3: Modeling Using Geometric Similarity......Page 104
    2.4: Automobile Gasoline Mileage......Page 120
    2.5: Body Weight and Height, Strength and Agility......Page 123
    Introduction......Page 129
    3.1: Fitting Models to Data Graphically......Page 132
    3.2: Analytic Methods of Model Fitting......Page 139
    3.3: Applying the Least-Squares Criterion......Page 145
    3.4: Choosing a Best Model......Page 152
    Introduction......Page 161
    4.1: Harvesting in the Chesapeake Bay and Other One-Term Models......Page 162
    4.2: High-Order Polynomial Models......Page 172
    4.3: Smoothing: Low-Order Polynomial Models......Page 181
    4.4: Cubic Spline Models......Page 193
    Introduction......Page 209
    5.1: Simulating Deterministic Behavior: Area under a Curve......Page 211
    5.2: Generating Random Numbers......Page 215
    5.3: Simulating Probabilistic Behavior......Page 219
    5.4: Inventory Model: Gasoline and Consumer Demand......Page 227
    5.5: Queuing Models......Page 237
    6.1: Probabilistic Modeling with Discrete Systems......Page 248
    6.2: Modeling Component and System Reliability......Page 254
    6.3: Linear Regression......Page 257
    Introduction......Page 266
    7.1: An Overview of Optimization Modeling......Page 267
    7.2: Linear Programming I: Geometric Solutions......Page 279
    7.3: Linear Programming II: Algebraic Solutions......Page 289
    7.4: Linear Programming III: The Simplex Method......Page 293
    7.5: Linear Programming IV: Sensitivity Analysis......Page 303
    7.6: Numerical Search Methods......Page 309
    Introduction......Page 322
    8.1: Graphs as Models......Page 323
    8.2: Describing Graphs......Page 330
    8.3: Graph Models......Page 332
    8.4: Using Graph Models to Solve Problems......Page 347
    8.5: Connections to Mathematical Programming......Page 356
    Introduction......Page 363
    9.1: Probability and Expected Value......Page 365
    9.2: Decision Trees......Page 372
    9.3: Sequential Decisions and Conditional Probabilities......Page 381
    9.4: Decisions Using Alternative Criteria......Page 391
    10.1: Game Theory: Total Conflict......Page 402
    10.2: Total Conflict as a Linear Program Model: Pure and Mixed Strategies......Page 412
    10.3: Decision Theory Revisited: Games against Nature......Page 431
    10.4: Alternative Methods for Determining Pure Strategy Solutions......Page 439
    10.5: Alternative Shortcut Solution Methods for the 2 x 2 Total Conflict Game......Page 446
    10.6: Partial Conflict Games: The Classical Two-Player Games......Page 454
    10.7: Illustrative Modeling Examples......Page 465
    Introduction......Page 482
    11.1: Population Growth......Page 485
    11.2: Prescribing Drug Dosage......Page 495
    11.3: Braking Distance Revisited......Page 503
    11.4: Graphical Solutions of Autonomous Differential Equations......Page 507
    11.5: Numerical Approximation Methods......Page 515
    11.6: Separation of Variables......Page 524
    11.7: Linear Equations......Page 536
    Introduction......Page 548
    12.1: Graphical Solutions of Autonomous Systems of First-Order Differential Equations......Page 549
    12.2: A Competitive Hunter Model......Page 554
    12.3: A Predator-Prey Model......Page 563
    12.4: Two Military Examples......Page 572
    12.5: Euler's Method for Systems of Differential Equations......Page 583
    Introduction......Page 593
    13.1: An Inventory Problem: Minimizing the Cost of Delivery and Storage......Page 594
    13.2: Methods to Optimize Functions of Several Variables......Page 602
    13.3: Constrained Continuous Optimization......Page 611
    13.4: Managing Renewable Resources: The Fishing Industry......Page 616
    Introduction......Page 625
    14.1: Dimensions as Products......Page 628
    14.2: The Process of Dimensional Analysis......Page 636
    14.3: A Damped Pendulum......Page 645
    14.4: Examples Illustrating Dimensional Analysis......Page 651
    14.5: Similitude......Page 661
    15.1: An Arms Race......Page 667
    15.2: Modeling an Arms Race in Stages......Page 680
    15.3: Managing Nonrenewable Resources: The Energy Crisis......Page 684
    15.4: Effects of Taxation on the Energy Crisis......Page 688
    15.5: A Gasoline Shortage and Taxation......Page 692
    1985: The Strategic Reserve Problem......Page 697
    1986: The Emergency-Facilities Location Problem......Page 699
    1987: The Salt Storage Problem......Page 700
    1988: The Railroad Flatcar Problem......Page 701
    1988: The Drug Runner Problem......Page 702
    1989: The Midge Classification Problem......Page 703
    1990: The Brain-Drug Problem......Page 704
    1991: The Water Tank Problem......Page 705
    1991: The Steiner Tree Problem......Page 706
    1992: The Emergency Power-Restoration Problem......Page 707
    1992: The Air-Traffic-Control Radar Problem......Page 709
    1993: The Optimal Composting Problem
    ......Page 710
    1994: The Concrete Slab Problem......Page 711
    1994: The Communications Network Problem......Page 712
    1995: The Single Helix......Page 715
    1995: Aluacha Balaclava College......Page 716
    1996: The Contest Judging Problem......Page 718
    1997: The Velociraptor Problem......Page 719
    1997: Mix Well for Fruitful Discussions......Page 720
    1998: MRI Scanners......Page 721
    1999: Deep Impact......Page 722
    2000: Air Traffic Control......Page 723
    2000: Radio Channel Assignments......Page 724
    2001: Choosing a Bicycle Wheel......Page 725
    2001: Escaping a Hurricane's Wrath......Page 726
    2002: Airline Overbooking......Page 727
    2003: Gamma Knife Treatment Planning......Page 728
    2004: Are Fingerprints Unique?......Page 729
    2005: Tollbooths......Page 730
    2006: Wheelchair Access at Airports......Page 731
    2007: Gerrymandering......Page 732
    2008: Take a Bath......Page 733
    2009: Energy and the Cell Phone......Page 734
    2010: The Sweet Spot......Page 735
    2011: Repeater Coordination......Page 736
    2012: Camping along the Big Long River......Page 737
    Appendix B: An Elevator Simulation Algorithm......Page 739
    Pivoting by Matrix Inversion and Multiplication......Page 747
    The Revised Simplex Method......Page 748
    Integration by Parts......Page 750
    Partial Fractions......Page 753
    Answers to Selected Problems......Page 757
    Index......Page 784

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