Principles of mathematical modeling / Clive L. Dym.
Editor: Amsterdam : Elsevier Academic Press, c2004Edición: 2nd edDescripción: xviii, 303 p. : il. ; 24 cmISBN: 0122265513Tema(s): Mathematical modelsOtra clasificación: 00A71 (01-01 00A69 00A73 41A10 62-99 65D10) Recursos en línea: Table of contents | Publisher descriptionPreface xiii Acknowledgments xvii PART A: Foundations [1] CHAPTER 1 What Is Mathematical Modeling? [3] 1.1 Why Do We Do Mathematical Modeling? [4] 1.1.1 Mathematical Modeling and the Scientific Method [4] 1.1.2 Mathematical Modeling and the Practice of Engineering [5] 1.2 Principles of Mathematical Modeling [6] 1.3 Some Methods of Mathematical Modeling [8] 1.3.1 Dimensional Homogeneity and Consistency [9] 1.3.2 Abstraction and Scaling [9] 1.3.3 Conservation and Balance Principles [10] 1.3.4 Constructing Linear Models [11] 1.4 Summary [11] 1.5 References [12] CHAPTER 2 Dimensional Analysis [13] 2.1 Dimensions and Units [14] r 2.2 Dimensional Homogeneity [15] 2.3 Why Do We Do Dimensional Analysis? [16] 2.4 How Do We Do Dimensional Analysis? [19] 2.4.1 The Basic Method of Dimensional Analysis [20] 2.4.2 The Buckingham Pi Theorem for Dimensional Analysis [24] 2.5 Systems of Units [28] 2.6 Summary [30] 2.7 References [31] 2.8 Problems [31] CHAPTER 3 Scale [33] 3.1 Abstraction and Scale [33] 3.2 Size and Shape: Geometric Scaling [35] 3.2.1 Geometric Scaling and Flight Muscle Fractions in Birds [36] 3.2.2 Linearity and Geometric Scaling [37] 3.2.3 "Log-log" Plots of Geometric Scaling Data [38] 3.3 Size and Function-I: Birds and Flight [44] 3.3.1 The Power Needed for Hovering [45] 3.3.2 The Power Available for Hovering [46] 3.3.3 So There Is a Hovering Limit [47] 3.4 Size and Function-ll: Hearing and Speech [47] 3.4.1 Hearing Depends on Size [48] 3.4.2 Speech Depends on Size [50] 3.5 Size and Limits: Scale in Equations [51] 3.5.1 When a Model Is No Longer Applicable [52] 3.5.2 Scaling in Equations [52] 3.5.3 Characteristic Times [54] 3.6 Consequences of Choosing a Scale [55] 3.6.1 Scaling and Data Acquisition [55] 3.6.2 Scaling and the Design of Experiments [59] 3.6.3 Scaling and Perceptions of Presented Data [62] 3.7 Summary [65] 3.8 References [66] 3.9 Problems [67] CHAPTER 4 Approximating and Validating Models [71] 4.1 Taylor's Formula [71] 4.1.1 Taylor's Formula and Series [72] 4.1.2 Taylor Series of Trigonometric and Hyperbolic Functions [74] 4.1.3 Binomial Expansions [78] 4.2 Algebraic Approximations [82] 4.3 Numerical Approximations: Significant Figures [84] 4.4 Validating the Model-I: How Do We Know the Model Is OK? [88] 4.4.1 Checking Dimensions and Units [89] 4.4.2 Checking Qualitative and Limit Behavior [91] 4.5 Validating the Model-ll: How Large Are the Errors? [92] 4.5.1 Error [93] 4.5.2 Accuracy and Precision [94] 4.6 Fitting Curves to Data [96] 4.7 Elementary Statistics [99] 4.7.1 Mean, Median, and Standard Deviation [100] 4.7.2 Histograms [102] 4.8 Summary [106] 4.9 Appendix: Elementary Transcendental Functions [107] 4.10 References [110] 4.11 Problems [111] PART B: Applications [115] CHAPTER 5 Exponential Growth and Decay [117] 5.1 How Do Things Get So Out of Hand? [117] 5.2 Exponential Functions and Their Differential Equations [122] 5.2.1 Calculating and Displaying Exponential Functions [122] 5.2.2 The First-Order Differential Equation dN/dt-λN = 0 [126] 5.3 Radioactive Decay [127] 5.4 Charging and Discharging a Capacitor [130] 5.4.1 A Capacitor Discharges [131] 5.4.2 A Capacitor Is Charged [133] 5.5 Exponential Models in Money Matters [136] 5.5.1 Compound Interest [136] 5.5.2 Inflation [138] 5.6 A Nonlinear Model of Population Growth [141] 5.7 A Coupled Model of Fighting Armies [144] 5.8 Summary [147] 5.9 References [147] 5.10 Problems [148] CHAPTER 6 Traffic Flow Models [151] 6.1 Can We Really Make Sense of Freeway Traffic? [151] 6.2 Macroscopic Traffic Flow Models [152] 6.2.1 Conservation of Cars [153] 6.2.2 Relating Traffic Speed to Traffic Density [155] 6.2.3 Relating Traffic Flow to Traffic Density: The Fundamental Diagram [156] 6.2.4 The Continuum Hypothesis in Macroscopic Traffic Modeling [159] 6.3 Microscopic Traffic Models [162] 6.3.1 An Elementary, Linear Car-following Model [162] 6.3.2 An Alternate Derivation of the Same Model [169] 6.3.3 Comments on Car-following Models [170] 6.4 Summary [171] 6.5 References [171] 6.6 Problems [172] CHAPTER 7 Modeling Free Vibration [175] 7.1 The Freely-Vibrating Pendulum-I: Formulating a Model [176] 7.1.1 Some Experimental Results [176] 7.1.2 Dimensional Analysis [178] 7.1.3 Equations of Motion [179] 7.1.4 More Dimensional Analysis [182] 7.1.5 Conserving Energy as the Pendulum Moves [184] 7.1.6 Dissipating Energy as the Pendulum Moves [186] 7.2 The Freely-Vibrating Pendulum-ll: The Linear Model [188] 7.2.1 Linearizing the Nonlinear Model [188] 7.2.2 The Differential Equation md2x/dt2 + kx = 0 [191] 7.2.3 The Linear Model [192] 7.3 The Spring-Mass Oscillator-I: Physical Interpretations [194] 7.4 Stability of a Two-mass Pendulum [195] 7.5 The Freely-Vibrating Pendulum-Ill: The Nonlinear Model [199] 7.6 Modeling the Population Growth of Coupled Species [201] 7.6.1 Qualitative Solution for the Nonlinear Model [203] 7.6.2 Oscillatory Solution for the Linearized Model [204] 7.7 Summary [206] 7.8 References [207] 7.9 Problems [208] CHAPTER 8 Applying Vibration Models [211] 8.1 The Spring-Mass Oscillator-ll: Extensions and Analogies [212] 8.1.1 Restoring and Dissipative Forces and Elements [215] 8.1.2 Electric Circuits and the Electrical-Mechanical Analogy [216] 8.2 The Fundamental Period of a Tall, Slender Building [221] 8.3 The Cyclotron Frequency [225] 8.4 The Fundamental Frequency of an Acoustic Resonator [228] 8.5 Forcing Vibration: Modeling an Automobile Suspension [232] 8.6 The Differential Equation md2x/dt2 + kx = F(f) [234] 8.7 Resonance and Impedance in Forced Vibration [236] 8.8 Summary [240] 8.9 References [241] 8.10 Problems [242] CHAPTER 9 Optimization: What Is the Best [247] 9.1 Continuous Optimization Modeling [248] 9.2 Optimization with Linear Programming [253] 9.2.1 Maximizing Profit in the Furniture Business [255] 9.2.2 On Linear Programming and Extensions [258] 9.2.3 On Defining and Assessing Optima [259] 9.3 The Transportation Problem [260] 9.4 Choosing the Best Alternative [265] 9.4.1 Rankings and Pairwise Comparisons [265] 9.4.2 Borda Counts and Pairwise Comparisons [267] 9.4.3 Pairwise Comparisons and Rank Reversals [270] 9.4.4 Pay Attention to All of the Data [271] 9.4.5 On Pairwise Comparisons and Making Decisions [273] 9.5 A Miscellany of Optimization Problems [275] 9.5.1 Is There Enough Energy to Create a Sphere? [276] 9.5.2 Maximizing the Range of Planes and Birds [278] 9.5.3 Geometric Programming for a Plane's Optimum Speed [282] 9.5.4 The Lightest Diving Board (or Cantilever Beam) [286] 9.6 Summary [290] 9.7 References [291] 9.8 Problems [293] Index [297]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A71 D997 (Browse shelf) | Available | A-8491 |
Incluye referencias bibliográficas e índice.
Preface xiii --
Acknowledgments xvii --
PART A: Foundations [1] --
CHAPTER 1 What Is Mathematical Modeling? [3] --
1.1 Why Do We Do Mathematical Modeling? [4] --
1.1.1 Mathematical Modeling and the Scientific Method [4] --
1.1.2 Mathematical Modeling and the Practice of Engineering [5] --
1.2 Principles of Mathematical Modeling [6] --
1.3 Some Methods of Mathematical Modeling [8] --
1.3.1 Dimensional Homogeneity and Consistency [9] --
1.3.2 Abstraction and Scaling [9] --
1.3.3 Conservation and Balance Principles [10] --
1.3.4 Constructing Linear Models [11] --
1.4 Summary [11] --
1.5 References [12] --
CHAPTER 2 Dimensional Analysis [13] --
2.1 Dimensions and Units [14] --
r 2.2 Dimensional Homogeneity [15] --
2.3 Why Do We Do Dimensional Analysis? [16] --
2.4 How Do We Do Dimensional Analysis? [19] --
2.4.1 The Basic Method of Dimensional Analysis [20] --
2.4.2 The Buckingham Pi Theorem for --
Dimensional Analysis [24] --
2.5 Systems of Units [28] --
2.6 Summary [30] --
2.7 References [31] --
2.8 Problems [31] --
CHAPTER 3 Scale [33] --
3.1 Abstraction and Scale [33] --
3.2 Size and Shape: Geometric Scaling [35] --
3.2.1 Geometric Scaling and Flight Muscle Fractions in Birds [36] --
3.2.2 Linearity and Geometric Scaling [37] --
3.2.3 "Log-log" Plots of Geometric Scaling Data [38] --
3.3 Size and Function-I: Birds and Flight [44] --
3.3.1 The Power Needed for Hovering [45] --
3.3.2 The Power Available for Hovering [46] --
3.3.3 So There Is a Hovering Limit [47] --
3.4 Size and Function-ll: Hearing and Speech [47] --
3.4.1 Hearing Depends on Size [48] --
3.4.2 Speech Depends on Size [50] --
3.5 Size and Limits: Scale in Equations [51] --
3.5.1 When a Model Is No Longer Applicable [52] --
3.5.2 Scaling in Equations [52] --
3.5.3 Characteristic Times [54] --
3.6 Consequences of Choosing a Scale [55] --
3.6.1 Scaling and Data Acquisition [55] --
3.6.2 Scaling and the Design of Experiments [59] --
3.6.3 Scaling and Perceptions of Presented Data [62] --
3.7 Summary [65] --
3.8 References [66] --
3.9 Problems [67] --
CHAPTER 4 Approximating and Validating --
Models [71] --
4.1 Taylor's Formula [71] --
4.1.1 Taylor's Formula and Series [72] --
4.1.2 Taylor Series of Trigonometric and Hyperbolic Functions [74] --
4.1.3 Binomial Expansions [78] --
4.2 Algebraic Approximations [82] --
4.3 Numerical Approximations: Significant Figures [84] --
4.4 Validating the Model-I: How Do We Know the Model Is OK? [88] --
4.4.1 Checking Dimensions and Units [89] --
4.4.2 Checking Qualitative and Limit Behavior [91] --
4.5 Validating the Model-ll: How Large Are the Errors? [92] --
4.5.1 Error [93] --
4.5.2 Accuracy and Precision [94] --
4.6 Fitting Curves to Data [96] --
4.7 Elementary Statistics [99] --
4.7.1 Mean, Median, and Standard Deviation [100] --
4.7.2 Histograms [102] --
4.8 Summary [106] --
4.9 Appendix: Elementary Transcendental Functions [107] --
4.10 References [110] --
4.11 Problems [111] --
PART B: Applications [115] --
CHAPTER 5 Exponential Growth and Decay [117] --
5.1 How Do Things Get So Out of Hand? [117] --
5.2 Exponential Functions and Their Differential Equations [122] --
5.2.1 Calculating and Displaying Exponential Functions [122] --
5.2.2 The First-Order Differential Equation dN/dt-λN = 0 [126] --
5.3 Radioactive Decay [127] --
5.4 Charging and Discharging a Capacitor [130] --
5.4.1 A Capacitor Discharges [131] --
5.4.2 A Capacitor Is Charged [133] --
5.5 Exponential Models in Money Matters [136] --
5.5.1 Compound Interest [136] --
5.5.2 Inflation [138] --
5.6 A Nonlinear Model of Population Growth [141] --
5.7 A Coupled Model of Fighting Armies [144] --
5.8 Summary [147] --
5.9 References [147] --
5.10 Problems [148] --
CHAPTER 6 Traffic Flow Models [151] --
6.1 Can We Really Make Sense of Freeway Traffic? [151] --
6.2 Macroscopic Traffic Flow Models [152] --
6.2.1 Conservation of Cars [153] --
6.2.2 Relating Traffic Speed to Traffic Density [155] --
6.2.3 Relating Traffic Flow to Traffic Density: The Fundamental Diagram [156] --
6.2.4 The Continuum Hypothesis in Macroscopic Traffic Modeling [159] --
6.3 Microscopic Traffic Models [162] --
6.3.1 An Elementary, Linear Car-following Model [162] --
6.3.2 An Alternate Derivation of the Same Model [169] --
6.3.3 Comments on Car-following Models [170] --
6.4 Summary [171] --
6.5 References [171] --
6.6 Problems [172] --
CHAPTER 7 Modeling Free Vibration [175] --
7.1 The Freely-Vibrating Pendulum-I: Formulating a Model [176] --
7.1.1 Some Experimental Results [176] --
7.1.2 Dimensional Analysis [178] --
7.1.3 Equations of Motion [179] --
7.1.4 More Dimensional Analysis [182] --
7.1.5 Conserving Energy as the Pendulum Moves [184] --
7.1.6 Dissipating Energy as the Pendulum Moves [186] --
7.2 The Freely-Vibrating Pendulum-ll: The Linear Model [188] --
7.2.1 Linearizing the Nonlinear Model [188] --
7.2.2 The Differential Equation md2x/dt2 + kx = 0 [191] --
7.2.3 The Linear Model [192] --
7.3 The Spring-Mass Oscillator-I: Physical Interpretations [194] --
7.4 Stability of a Two-mass Pendulum [195] --
7.5 The Freely-Vibrating Pendulum-Ill: The Nonlinear Model [199] --
7.6 Modeling the Population Growth of Coupled Species [201] --
7.6.1 Qualitative Solution for the Nonlinear Model [203] --
7.6.2 Oscillatory Solution for the Linearized Model [204] --
7.7 Summary [206] --
7.8 References [207] --
7.9 Problems [208] --
CHAPTER 8 Applying Vibration Models [211] --
8.1 The Spring-Mass Oscillator-ll: Extensions and Analogies [212] --
8.1.1 Restoring and Dissipative Forces and Elements [215] --
8.1.2 Electric Circuits and the Electrical-Mechanical Analogy [216] --
8.2 The Fundamental Period of a Tall, Slender Building [221] --
8.3 The Cyclotron Frequency [225] --
8.4 The Fundamental Frequency of an Acoustic Resonator [228] --
8.5 Forcing Vibration: Modeling an Automobile Suspension [232] --
8.6 The Differential Equation md2x/dt2 + kx = F(f) [234] --
8.7 Resonance and Impedance in Forced Vibration [236] --
8.8 Summary [240] --
8.9 References [241] --
8.10 Problems [242] --
CHAPTER 9 Optimization: What Is the Best [247] --
9.1 Continuous Optimization Modeling [248] --
9.2 Optimization with Linear Programming [253] --
9.2.1 Maximizing Profit in the Furniture Business [255] --
9.2.2 On Linear Programming and Extensions [258] --
9.2.3 On Defining and Assessing Optima [259] --
9.3 The Transportation Problem [260] --
9.4 Choosing the Best Alternative [265] --
9.4.1 Rankings and Pairwise Comparisons [265] --
9.4.2 Borda Counts and Pairwise Comparisons [267] --
9.4.3 Pairwise Comparisons and Rank Reversals [270] --
9.4.4 Pay Attention to All of the Data [271] --
9.4.5 On Pairwise Comparisons and Making Decisions [273] --
9.5 A Miscellany of Optimization Problems [275] --
9.5.1 Is There Enough Energy to Create a Sphere? [276] --
9.5.2 Maximizing the Range of Planes and Birds [278] --
9.5.3 Geometric Programming for a Plane's Optimum Speed [282] --
9.5.4 The Lightest Diving Board (or Cantilever Beam) [286] --
9.6 Summary [290] --
9.7 References [291] --
9.8 Problems [293] --
Index [297] --
Zbl, 1057.00008
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