05137nam 2200637 a 450 991045868860332120200520144314.01-280-96132-597866109613200-08-047028-9(CKB)1000000000364391(EBL)286730(OCoLC)162572033(SSID)ssj0000227390(PQKBManifestationID)11198006(PQKBTitleCode)TC0000227390(PQKBWorkID)10270109(PQKB)11459975(MiAaPQ)EBC286730(PPN)170263584(Au-PeEL)EBL286730(CaPaEBR)ebr10167048(CaONFJC)MIL96132(EXLCZ)99100000000036439120040316d2004 uy 0engur|n|---|||||txtccrPrinciples of mathematical modeling[electronic resource]2nd ed. /Clive L. Dym.Amsterdam ;Boston Elsevier Academic Pressc20041 online resource (323 p.)Description based upon print version of record.0-12-804744-5 0-12-226551-3 Includes bibliographical references and index.Contents; Preface; Acknowledgments; Part A: Foundations; 1 What is Mathematical Modeling?; 1.1 Why do we do mathematical modeling?; 1.2 Principles of mathematical modeling; 1.3 Some methods of methematical modeling; 1.4 Summary; 1.5 References; 2 Dimensional Analysis; 2.1 Dimensions and units; 2.2 Dimensional homogeneity; 2.3 Why do we do dimensional analysis?; 2.4 How do we do dimensional analysis?; 2.5 Systems of units; 2.6 Summary; 2.7 References; 2.8 Problems; 3 Scale; 3.1 Abstraction and scale; 3.2 Size and shape: geometric scaling; 3.3 Size and function-I: Birds and flight3.4 Size and function-II: Hearing and speech3.5 Size and limits: scale in equations; 3.6 Consequences of choosing a scale; 3.7 Summary; 3.8 References; 3.9 Problems; 4 Approximating and Validating MOdels; 4.1 Taylor's formula; 4.2 Algebraic approximations; 4.3 Numerical approximations: significant figures; 4.4 Validating the model-I: How do we know the model is OK?; 4.5 Validating the model-II: How large are the errors?; 4.6 Fitting curves to data; 4.7 Elementary statistics; 4.8 Summary; 4.9 Appendix: Elementary transcendental functions; 4.10 References; 4.11 Problems; Part B: Applications5 Exponential Growth and Decay5.1 How do things get so out of hand?; 5.2 Exponential functions and their differential equations; 5.3 Radioactive decay; 5.4 Charging and discharging a capacitor; 5.5 Exponential models in money matters; 5.6 A nonlinear model of population growth; 5.7 A coupled model of fighting armies; 5.8 Summary; 5.9 References; 5.10 Problems; 6 Traffic Flow Models; 6.1 Can we really make sense of freeway traffic?; 6.2 Macroscopic traffic flow models; 6.3 Microscopic traffic models; 6.4 Summary; 6.5 References; 6.6 Problems; 7 Modeling Free Vibration7.1 The freely-vibrating pendulum-I: Formulating a model7.2 The freely-vibrating pendulum-II: The linear model; 7.3 The spring-mass oscillator-I: Physical interpretations; 7.4 Stability of a two-mass pendulum; 7.5 The freely vibrating pendulum-III: The nonlinear model; 7.6 Modeling the popular growth of coupled species; 7.7 Summary; 7.8 References; 7.9 Problems; 8 Applying Vibration Models; 8.1 The spring-mass oscillator-II: Extensions and analogies; 8.2 The fundamental period of a tall, slender building; 8.3 The cyclotron frequency; 8.4 The fundamental frequency of an acoustic resonator8.5 Forcing vibration: modeling an automobile suspension8.6 The differential equation md2x/dt2+kx=F(t_; 8.7 Resonance and impedance in forced vibration; 8.8 Summary; 8.9 References; 8.10 Problems; 9 Optimization: What Is the Best...?; 9.1 Continuous optimization modelling; 9.2 Optimization with linear programming; 9.3 The transportation problem; 9.4 Choosing the best alternative; 9.5 A miscellany of optimization problems; 9.6 Summary; 9.7 References; 9.8 Problems; IndexScience and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and ""own"" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introMathematical modelsElectronic books.Mathematical models.511/.8Dym Clive L41312MiAaPQMiAaPQMiAaPQBOOK9910458688603321Principles of mathematical modeling348110UNINA