Mathematical modelling: a case studies approach
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2005
|
| Schriftenreihe: | Student mathematical library
27 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XVI, 196 S. Ill., graph. Darst. |
| ISBN: | 0821836501 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical modelling |b a case studies approach |c Reinhard Illner ... |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2005 | |
| 300 | |a XVI, 196 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v 27 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Modèles mathématiques | |
| 650 | 4 | |a Modèles mathématiques - Problèmes et exercices | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
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Datensatz im Suchindex
| _version_ | 1804133374515740672 |
|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
Crystallization Dynamics
1
§1.1.
Derivation of the K-A Model
3
§1.2.
Emergence of the
Poisson
Distribution from the
Binomial Distribution
6
§1.3.
Testing the
K
-А
Model
7
§1.4.
A New Model
8
§1.5.
The Averaging Process
11
§1.6.
Choosing the Probability Density
ƒ 11
§1.7.
Why Did the
K
-А
Model Fail?
15
Exercises
15
Notes
20
Chapter
2.
Will the Valve Hold0
21
§2.1.
Terminology
23
§2.2.
The Relevant Forces
24
§2.3.
The Equation of Motion
26
§2.4.
Analysis: Is the Initial Value Problem Well-Posed?
27
§2.5.
Revising the Model
28
VII
viii Contents
§2.6. Revision 1:
Adding a Reference Distance
31
§2.7.
Revision
2:
Changing the Initial Conditions
32
§2.8.
PmaX: The Maximal Pressure
34
Exercises
37
Notes
39
Chapter
3.
How Much Will that Annuity Cost Me?
41
§3.1.
Interest Basics
41
§3.2.
Mortgages
43
§3-3.
Loan Repayment
49
§3.4.
Present Value
50
§3.5.
Annuities
50
§3.6.
Hazard Rate Functions
51
§3.7.
Expected Lifetime
56
§3.8.
An Annuity Problem
57
§3.9.
V(Y): How the Expected Value of the Annuity Varies
59
Exercises
60
Chapter
4.
Dimensional Analysis
63
§4.1.
A Classical Example: The Pendulum
63
§4.2.
Dimensional Analysis: The General Procedure
67
§4.3.
The Energy Released by a Nuclear Bomb
70
§4.4.
Exploration: How to Cook a Turkey
74
Exercises
81
Chapter
5.
Predator-Prey Systems
83
§5-1.
The
Lotka-
Voìterra
Model
83
§5.2.
The Effect of Interference on the System
87
§5.3.
Linearization: The General Procedure
92
§5.4.
Solving Linear Systems
95
§5.5.
Classification of the Equilibria
98
§5.6.
The Phase Paths
101
Contents ix
§5.7. Multiple
Species
104
§5.8.
Exploration A:
Structural Stability
105
§5.9.
Exploration
В:
The
Lorenz Attractor 110
Exercises
114
Chapter
6.
A Control Problem in Fishery Management
119
§6.1.
Variables and Parameters
120
§6.2.
The Logistic Growth Model
120
§6.3.
Maximizing the Sustainable Catch
122
§6.4.
Maximizing the Profit
125
Exercises
129
Chapter
7.
Formal Justice
131
§7.1.
The Basic Functional Equation
131
§7.2.
Formal Justice: A Generalized Approach
136
§7.3.
Multiple Qualifications
138
§7.4.
Exploration: Exotic Solutions of Cauchy s Functional
Equation
142
Exercises
146
Chapter
8.
Traffic Dynamics: A Microscopic Model
149
§8.1.
The Braking Force
149
§8.2.
Density and Flux at Equilibrium
151
§8.3.
A Case Study: Propagation of a Perturbation
156
§8.4.
Exploration:
Peano*s
Existence Theorem
163
Exercises
167
Chapter
9.
Traffic Dynamics: Macroscopic Modelling
169
§9.1.
Scalar Conservation Laws
170
§9.2.
Solving Initial Value Problems for First-Order PDEs
173
§9.3.
The Green Light Problem
178
§9.4.
Smooth Initial Data, and General Scalar Conservation
Laws
183
χ
Contents
§9.5.
Intersecting Characteristics
184
Exercises
193
Bibliography
195
Mathematical modelling is a subject without boundaries. It is the
means by which mathematics becomes useful to virtually any subject.
Moreover, modelling has been and continues to be a driving force for
the development of mathematics itself. This book explains the
process of modelling real situations to obtain mathematical problems
that can be analyzed, thus solving the original problem.
The presentation is in the form of case studies, which are developed
much as they would be in true applications. In many cases, an initial
model is created, then modified along the way. Some cases are
familiar, such as the evaluation of an annuity. Others are unique, such
as the fascinating situation in which an engineer, armed only with a
slide rule, had
24
hours to compute whether a valve would hold
when a temporary rock plug was removed from a water tunnel.
Each chapter ends with a set of exercises and some suggestions for
class projects. Some projects are extensive, as with the explorations
of the predator-prey model; others are more modest.
The text was designed to be suitable for a one-term course for
advanced undergraduates. The selection of topics and the style of
exposition reflect this choice. The authors have also succeeded in
demonstrating just how enjoyable the subject can be.
This is an ideal text for classes on modelling. It can also be used in
seminars or as preparation for mathematical modelling competitions.
|
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| dewey-full | 511/.8 511.8 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 0821836501 |
| language | English |
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| spelling | Mathematical modelling a case studies approach Reinhard Illner ... Providence, RI American Mathematical Society 2005 XVI, 196 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 27 Hier auch später erschienene, unveränderte Nachdrucke Modèles mathématiques Modèles mathématiques - Problèmes et exercices Wiskundige modellen gtt Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf (DE-588)4144384-6 Beispielsammlung gnd-content Mathematisches Modell (DE-588)4114528-8 s DE-604 Illner, Reinhard 1950- Sonstige (DE-588)1019618892 oth Student mathematical library 27 (DE-604)BV013184751 27 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180970&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180970&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mathematical modelling a case studies approach Student mathematical library Modèles mathématiques Modèles mathématiques - Problèmes et exercices Wiskundige modellen gtt Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4144384-6 |
| title | Mathematical modelling a case studies approach |
| title_auth | Mathematical modelling a case studies approach |
| title_exact_search | Mathematical modelling a case studies approach |
| title_full | Mathematical modelling a case studies approach Reinhard Illner ... |
| title_fullStr | Mathematical modelling a case studies approach Reinhard Illner ... |
| title_full_unstemmed | Mathematical modelling a case studies approach Reinhard Illner ... |
| title_short | Mathematical modelling |
| title_sort | mathematical modelling a case studies approach |
| title_sub | a case studies approach |
| topic | Modèles mathématiques Modèles mathématiques - Problèmes et exercices Wiskundige modellen gtt Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Modèles mathématiques Modèles mathématiques - Problèmes et exercices Wiskundige modellen Mathematisches Modell Mathematical models Beispielsammlung |
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