Principles of Mathematical Modeling, Second Edition

322 Pages·2004·2.73 MB·English

by  Clive Dym

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PRINCIPLESO F
MATHEMATICAL
MODELING
SeconEdd ition
CliLv.De y m
HarveMyu ddC ollege
ClaremoCnatl,if ornia
Amsterdam • Boston • Heidelbe•rg London • New York• Oxford
Paris • SanD iego• S anF rancisc•o S ingapo• reS ydney• Tokyo
ELSEVIER
ACADEMIC
PRESS
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Contents
Preface xiii
.................................................................... .
Acknowledgments . . xvii
................................................... .
PARTA :F oundations . 1
...............................................
CHAPTER1 WhatI sM athematicMaold eling?. 3
........
11. Why Do We Do MathematicMaold eling? . 4
.................
11.1. MathemaitcaMlo delinagn dt heS cientific
Method ......................................4. ...........
.,
11.2. MathematicMaold elign andt heP ractiocfe
Engineering . . . . . 5
............... .. .........................
12. Princliepso fM athematicMaold eling 6
........................
13. Some Methodosf M athematicMaold eling . 8
...............
13..1 DimensionHaolm ogeneiatnyd C onsistency 9
......
13..2 AbstractainodnS calin.g. . . . .. . 9
.. ... .. ..... ...........
13..3 ConservatainodnB alancPer inciples 1 0
..............
13..4 ConstructLiinnge aMro dels . . . 11
.......................
14. Summary . . . . . . 11
........... ............................ ............
15. Reference.s . . . 12
...................................................
vii
viii Contents
CHAPTER2 DimensionAanla lysi.s ... ..13
. ............. ... . .
2.1 Dimensioannsd U nits. ....................1.4. ..................
2.2 DimensionHaolm ogeneity. . . . 15
... ............................
2.3 Why Do We Do DimensionAanla lysis? .. 16
..................
2.4 How Do We Do DimensionAanla lysis? . 19
...................
2.4.1T heB asiMce thodo fD imensionAanla lys.i.s. 2.0. .
2.4.2T heB uckinghaPmiT heoremf or
DimensionAanla lysi.s. . . . . 24
. .. . .......................
2.5 SystemosfUnits . . . .. .. . 28
................. .... ...................
2.6 Summary 30
.........................................................
2.7 Reference.s . . . ... .. . . 31
... ... ................ ......................
2.8 Problem.s. . . . . . . .. 31
. .................... ................. .. .. . ....
CHAPTER3 Scale .... ..... . .. ..3 3
.... .. ........ . ................... ..
3.1 AbstractainodnS cale . . . . 33
............ ..........................
3.2 Sizea ndS hapeG:e ometric Sc.alin.g . . 35
............ .........
3.2.1G eometriScc alinagn dF ligMhuts cle
FractioinnBs i rds . .. 36
....................................
3.2.2L inearaintdyG eometriScc aling . 37
...................
3.2.3" Log-logP"l otosf G eometriScc alinDga ta 38
.......
3.3 Sizea ndF unctionB-iIr:d s and Fl.i..g.ht . .4 4
.. . ..............
3.3.1 TheP owerN eedefdo rH overi.n.g. .......4.5. ........
3.3.2T heP owerA vailabfolreH overi.n.g.. ......4.6. ......
3.3.3S oT hereI sa HoverinLgi mit..... .........4.7. .........
3.4 Sizea ndF unctionH-eIaIr:i nagn dS peech. ........4.7. .....
3.4.1H earinDge pendosn Siz.e. . . . 48
............... .........
3.4.2S peechD ependosn Si.ze .... 50
..... ...................
3.5 Sizea ndL imitSsc:a lien E quations 51
.........................
3.51. When a ModeIlsN o LongeArp plicable . 52
..........
3.5.2S calinignE quation.s. .. . .. . 52
... . ........ ...............
3.5.3C haracteriTismteisc. .........................5..4. ......
3.6 ConsequencoefsC hoosinag S cale. ... .... 55
. .. . .... .........
3.6.1S calinagn d DaAtcaq uisition. .. . 55
........ . ...........
3.6.2S calinagn dt heD esigonf E xperimen.ts 59
..........
3.6.3 Scalinagn dP erceptioofnP sr esentDeadt a 62
.......
3.7 Summary . . . .. .. 65
............................ ...... ................
3.8 References .. .. . . 66
.............. . ..................................
3.9 Problems . . . 67
........................... ...........................
CHAPTER4 ApproximatainndgV aliadting
Models ... . . 71
..........................................
4.1 TaylorF'osr mul.a . .. . .. . . 71
............. ......... .................
Contents ix
4..11 TaylorF'osr mulaan dS eries . . 72
..................... ..
4..12 TayloSre rieosfT rigonometarnidc
HyperbolFiucn ctions .. . . ..7 4
...... ......................
4..13 BinomiaElx pansio.ns. . . . 78
..... ........................
4.2 AlgebraAipcp roximatio.ns . . . ... ..82
.. ...... ... .. ....... .. .... .
4.3 NumericAaplp roximatiSoingsn:i ficFaingtu re.s .. 84
. .. . ..
4.4 ValidattihnegM odel-HIo:w Do We Know
theM odelI sO K? . .. . 88
. ........... .......... .....................
4.4.1C heckinDgi mensioannsd Units . .8 9
..................
4.4.2C heckinQgu alitatainvdeL imit Beha.vior. 91
....... .
4.5 ValidattihnegM odel-IHIo:w LargAer et heE rrors? 92
.....
4.5.1E rror 93
.......................................................
4.5.2A ccuracayn dP recision. . . . 94
.... ....... .............. ..
4.6 Fitting CutroDv aetsa . . . . 96
........ ..............................
4.7 ElementaSrtya tis.t.i...c..s. ...................................9 9
4.7.1M ean,M ediana,n dS tandarDde viation . 100
........
4.7.2H istogram.s . . .1 02
. ... ....................................
4.8 Summary ... . .. . .. .. . . 106
... . ........... . .... ........ ............ ..
4.9 AppendiExl:e mentaTrrya nscendenFtuanlc tions. 1 07
....
4.10R eferences. . . . .. .. 110
....... .. .............. ......................
4.11P roblems. ... . . . .1 11
... . . .. ........... .............................
PARTB :A pplicatio.ns. .. . . ... .1 15
.. ...... . . ................ . .......
CHAPTER5 ExponentGiraolw tha ndD ecay 1 17
........
5.1 How Do ThingGse tS o Outo fH and?. .. . .117
. . . ............ .
5.2 ExponentFiuanlc tioannsd T heiDri fferential
Equations .. . . .. . .. .122
..... ...................... ........... .......
5.2.1C alclua tianngd D isplayiEnxgp onential
Functio.n.s . . 122
. . ........................... ..............
5.2.2T heF irst-OrDdieffre rentEiqaualt ion
dNI d t- AN 0 ............................1..2 .6. ......
=
5.3 RadioactDievcea y. . . . 127
........................................
5.4 Charginagn dD ischargian Cga pacito..r..". ............ 130
5.4.1A CapacitDoirs charges. .. .. . 131
..... . ........... .. ....
5.4.2A CapacitIosCr h arged . 133
.............................
5.5 ExponentMioadle lsi nM oneyM atters .1 36
..................
5.5.1C om poundI ntere.s.t . . .. .. 136
. .............. ..... ......
5.5.2I nflat.io.n . .. .. . . . . 138
............... . .. ...... ..............
5.6 A NonlineMaord elo fP opulatiGorno wth. . 141
.. .. .........
5.7 A CoupleMdo delo fF ightiAnrgm ies. . ..1 44
. ................
5.8 Summar.y .. .. .. . . . ...1 47
. ................ ..... ... .... .... ........ .