LEADER 05142nam 2200649 a 450 001 9910817454203321 005 20230822144330.0 010 $a1-280-96132-5 010 $a9786610961320 010 $a0-08-047028-9 035 $a(CKB)1000000000364391 035 $a(EBL)286730 035 $a(OCoLC)162572033 035 $a(SSID)ssj0000227390 035 $a(PQKBManifestationID)11198006 035 $a(PQKBTitleCode)TC0000227390 035 $a(PQKBWorkID)10270109 035 $a(PQKB)11459975 035 $a(Au-PeEL)EBL286730 035 $a(CaPaEBR)ebr10167048 035 $a(CaONFJC)MIL96132 035 $z(PPN)120577585 035 $a(PPN)170263584 035 $a(FR-PaCSA)45006560 035 $a(MiAaPQ)EBC286730 035 $a(EXLCZ)991000000000364391 100 $a20040316d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPrinciples of mathematical modeling 205 $a2nd ed. /$bClive L. Dym. 210 $aAmsterdam ;$aBoston $cElsevier Academic Press$dc2004 215 $a1 online resource (323 p.) 300 $aDescription based upon print version of record. 311 $a0-12-804744-5 311 $a0-12-226551-3 320 $aIncludes bibliographical references and index. 327 $aContents; 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 flight 327 $a3.4 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: Applications 327 $a5 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 Vibration 327 $a7.1 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 resonator 327 $a8.5 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; Index 330 $aScience 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 intro 606 $aMathematical models 615 0$aMathematical models. 676 $a511/.8 700 $aDym$b Clive L$041312 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817454203321 996 $aPrinciples of mathematical modeling$9348110 997 $aUNINA