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Principles of mathematical modeling / Clive L. Dym, Elizabeth S. Ivey.
- Format:
- Book
- Author/Creator:
- Dym, Clive L.
- Ivey, Elizabeth S., author.
- Series:
- Computer science and applied mathematics
- Language:
- English
- Subjects (All):
- Mathematical models.
- Physical Description:
- xiii, 260 pages : illustrations ; 25 cm.
- Place of Publication:
- New York : Academic Press, [1980]
- Contents:
- 2 Dimensional Analysis 11
- Dimensions and Units 11
- Dimensional Analysis
- Motivation 14
- The Process 17
- Units 24
- 3 Scaling 28
- Size and Shape 28
- Size and Function 33
- Size and Limits 38
- Consequences of Choosing a Scale 41
- 4 Approximation and Reasonableness of Answers 51
- Taylor Series 51
- Binomial Expansion 54
- Trigonometric Series 57
- Algebraic Approximations and Significant Figures 59
- Validating the Model
- Errors 63
- Averaging
- Mean, Median, Mode 66
- Curve Fitting: Least Squares Method; The Continuum Hypothesis 69
- Testing 77
- Part B Applications
- 5 Free Oscillations of a Pendulum 85
- Results of an Experiment 85
- Some Dimensional Analysis 87
- Equations of Motion 89
- More Dimensional Analysis 92
- Linear Model of the Pendulum 95
- Energy Considerations
- Conservation 97
- Dissipation 100
- Nonlinear Model of the Pendulum 103
- Appendix Transformation of Equations of Motion 110
- 6 Forced Motion of Linerr Oscillators 112
- The Spring-Mass Oscillator 112
- Building Vibration 116
- Automobile Suspension System 119
- Acoustic Resonator 122
- Particle Moving in a Magnetic Field 125
- Electrical Circuits and the Electrical-Mechanical Analogy 127
- Forced Motion of a Linear Oscillator: Resonance and Impedance 130
- 7 Traffic Flow Models 139
- Macroscopic Traffic Flow Theory
- I. Continuum Hypothesis 140
- II. The Fundamental Diagram 142
- Linear Car-Following Models 147
- Stability Analysis for Linear Car-Following Models 152
- Nonlinear Car-Following Models 154
- 8 Exponential Models 159
- Exponential Behavior 159
- Exponential Functions 164
- Radioactive Decay 167
- Discharge of a Capacitor in an RC Circuit 169
- Charging a Capacitor in an RC Circuit 171
- Inflation 172
- Compound Interest 173
- Growth in Demand for Highways 175
- Population Growth 177
- The Lotka-Volterra Equations 179
- Lanchester's Law 184
- 9 Operations Research: Linear Programming 190
- Optimization via the Calculus 193
- Optimization via Linear Programming 198
- The Transportation Problem 204
- Network Analysis 208
- 10 Diffraction and Scale 217
- Diffraction Geometry 218
- Diffraction Gratings 226
- X-Ray and Atomic Particle Diffraction 230
- Sound Wave Diffraction 234
- Appendix I Elementary Transcendental Functions 241
- Appendix II The Differential Equation dN/dt = [lambda]N 245
- Appendix III The Differential Equation m d[superscript 2]x/dt[superscript 2] + kx = F(t) 247.
- Notes:
- Includes index.
- Bibliography: pages 251-254.
- ISBN:
- 0122265505
- OCLC:
- 6112137
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